The People’s Share

GED Math

Algebra Practice 2

Multiplying binomials and factoring. 366 problems, in three parts, from one number times a group in parentheses to deciding for yourself which job a question wants. The answer key is at the end.

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This is a practice sheet, and it exists because these two skills are learned by repetition and nothing else. Quiz 39 explains both of them and asks ten questions. Ten is enough to find out whether you understand it. It is nowhere near enough to make it quick, and on the test it has to be quick.

So: 366 problems. Multiplying out in Part One, factoring in Part Two, and the two mixed together in Part Three. Each section begins with the plainest version and adds one thing.

Four words this sheet uses.

Three habits are worth building while you work.

Work in pencil. Do a section at a sitting rather than the whole sheet at once.

Part One

Multiplying out

Every question in this part is the same job: every term outside times every term inside. In sections 1 and 2 the outside is a single term; from section 3 on it is a whole binomial, and every term in the first binomial multiplies every term in the second. The sections add one difficulty at a time. Do them in order. If a section feels slow, stay in it; the next one assumes it.

1.One number times parentheses

A number outside the parentheses multiplies everything inside them — every term, not just the first.

Example3(x + 4) = 3x + 12.

Multiply out.

  1. 1.2(x + 2) =
  2. 2.6(x + 2) =
  3. 3.6(x + 4) =
  4. 4.6(x + 7) =
  5. 5.4(x − 3) =
  6. 6.3(x + 8) =
  7. 7.6(x + 9) =
  8. 8.2(x + 10) =
  9. 9.5(x + 10) =
  10. 10.8(x + 10) =
  11. 11.9(x + 10) =
  12. 12.5(x + 11) =
  13. 13.9(x + 12) =
  14. 14.3(x − 9) =
  15. 15.9(x − 7) =
  16. 16.4(x − 10) =
  17. 17.9(x − 10) =
  18. 18.2(x − 11) =

2.A variable times parentheses

The same job when the thing outside is a variable, or a number and a variable together. Remember that x × x = x².

Example2x(x + 5) = 2x² + 10x.

Multiply out.

  1. 19.2x(x + 2) =
  2. 20.2x(x + 4) =
  3. 21.2x(x + 5) =
  4. 22.5x(x + 3) =
  5. 23.6x(x + 5) =
  6. 24.3x(x − 2) =
  7. 25.4x(x − 2) =
  8. 26.4x(x − 3) =
  9. 27.4x(x + 8) =
  10. 28.5x(x + 8) =
  11. 29.2x(x − 5) =
  12. 30.3x(x − 5) =
  13. 31.5x(x + 9) =
  14. 32.2x(x − 6) =
  15. 33.6x(x − 5) =
  16. 34.5x(x − 8) =

3.Two binomials, both signs plus

Four multiplications every time. The two middle terms are like terms, so they gather into one.

Example(x + 2)(x + 5) = x² + 5x + 2x + 10 = x² + 7x + 10.

Multiply out, and gather the middle.

  1. 35.(x + 1)(x + 1) =
  2. 36.(x + 1)(x + 2) =
  3. 37.(x + 2)(x + 2) =
  4. 38.(x + 3)(x + 2) =
  5. 39.(x + 3)(x + 3) =
  6. 40.(x + 3)(x + 4) =
  7. 41.(x + 4)(x + 4) =
  8. 42.(x + 2)(x + 5) =
  9. 43.(x + 3)(x + 5) =
  10. 44.(x + 5)(x + 1) =
  11. 45.(x + 5)(x + 4) =
  12. 46.(x + 1)(x + 6) =
  13. 47.(x + 6)(x + 3) =
  14. 48.(x + 6)(x + 5) =
  15. 49.(x + 3)(x + 7) =
  16. 50.(x + 4)(x + 7) =
  17. 51.(x + 5)(x + 7) =
  18. 52.(x + 7)(x + 1) =
  19. 53.(x + 7)(x + 2) =
  20. 54.(x + 7)(x + 5) =
  21. 55.(x + 3)(x + 8) =
  22. 56.(x + 6)(x + 8) =
  23. 57.(x + 7)(x + 8) =
  24. 58.(x + 8)(x + 2) =
  25. 59.(x + 8)(x + 4) =
  26. 60.(x + 1)(x + 9) =
  27. 61.(x + 3)(x + 9) =
  28. 62.(x + 5)(x + 9) =
  29. 63.(x + 6)(x + 9) =
  30. 64.(x + 8)(x + 9) =

4.Two binomials, one sign minus

The sign belongs to the number and travels with it into every multiplication it is part of.

Example(x + 3)(x − 7) = x² − 7x + 3x − 21 = x² − 4x − 21.

Multiply out.

  1. 65.(x − 2)(x + 1) =
  2. 66.(x − 2)(x + 2) =
  3. 67.(x + 1)(x − 2) =
  4. 68.(x − 4)(x + 4) =
  5. 69.(x − 1)(x + 5) =
  6. 70.(x − 3)(x + 5) =
  7. 71.(x + 2)(x − 5) =
  8. 72.(x + 5)(x − 4) =
  9. 73.(x − 4)(x + 6) =
  10. 74.(x − 5)(x + 6) =
  11. 75.(x − 6)(x + 3) =
  12. 76.(x − 6)(x + 4) =
  13. 77.(x − 6)(x + 5) =
  14. 78.(x + 6)(x − 1) =
  15. 79.(x − 7)(x + 1) =
  16. 80.(x + 6)(x − 7) =
  17. 81.(x + 7)(x − 1) =
  18. 82.(x + 7)(x − 7) =
  19. 83.(x − 8)(x + 2) =
  20. 84.(x − 8)(x + 6) =
  21. 85.(x − 8)(x + 8) =
  22. 86.(x + 1)(x − 8) =
  23. 87.(x + 2)(x − 8) =
  24. 88.(x + 8)(x − 2) =
  25. 89.(x + 8)(x − 5) =
  26. 90.(x + 8)(x − 6) =
  27. 91.(x − 1)(x + 9) =
  28. 92.(x − 9)(x + 4) =
  29. 93.(x + 9)(x − 2) =
  30. 94.(x + 9)(x − 3) =

5.Two binomials, both signs minus

Two negatives multiplied together give a positive, so the last number comes out positive while the middle one stays negative.

Example(x − 2)(x − 6) = x² − 6x − 2x + 12 = x² − 8x + 12.

Multiply out.

  1. 95.(x − 1)(x − 2) =
  2. 96.(x − 2)(x − 1) =
  3. 97.(x − 2)(x − 4) =
  4. 98.(x − 3)(x − 4) =
  5. 99.(x − 4)(x − 1) =
  6. 100.(x − 4)(x − 3) =
  7. 101.(x − 1)(x − 5) =
  8. 102.(x − 5)(x − 1) =
  9. 103.(x − 5)(x − 3) =
  10. 104.(x − 5)(x − 6) =
  11. 105.(x − 2)(x − 7) =
  12. 106.(x − 3)(x − 7) =
  13. 107.(x − 7)(x − 3) =
  14. 108.(x − 7)(x − 4) =
  15. 109.(x − 1)(x − 8) =
  16. 110.(x − 4)(x − 8) =
  17. 111.(x − 8)(x − 2) =
  18. 112.(x − 8)(x − 4) =
  19. 113.(x − 8)(x − 6) =
  20. 114.(x − 8)(x − 8) =
  21. 115.(x − 9)(x − 1) =
  22. 116.(x − 9)(x − 3) =
  23. 117.(x − 9)(x − 6) =
  24. 118.(x − 9)(x − 9) =

6.The middle disappears

When the two numbers are the same size with opposite signs, the middle terms cancel each other out and vanish. What is left is a square minus a square.

Example(x + 5)(x − 5) = x² − 5x + 5x − 25 = x² − 25.

Multiply out.

  1. 119.(x + 2)(x − 2) =
  2. 120.(x + 3)(x − 3) =
  3. 121.(x + 4)(x − 4) =
  4. 122.(x + 5)(x − 5) =
  5. 123.(x + 8)(x − 8) =
  6. 124.(x + 9)(x − 9) =
  7. 125.(x + 10)(x − 10) =
  8. 126.(x + 11)(x − 11) =
  9. 127.(x + 12)(x − 12) =
  10. 128.(x + 13)(x − 13) =
  11. 129.(x + 14)(x − 14) =
  12. 130.(x + 16)(x − 16) =
  13. 131.(x + 18)(x − 18) =
  14. 132.(x + 19)(x − 19) =
  15. 133.(x + 20)(x − 20) =
  16. 134.(x + 22)(x − 22) =
  17. 135.(x + 24)(x − 24) =
  18. 136.(x + 25)(x − 25) =

7.Squaring a binomial

The small 2 belongs to the whole binomial, so (x + 4)² means (x + 4)(x + 4). It does not mean x² + 16. Write the binomial out twice before you start.

Example(x + 4)² = (x + 4)(x + 4) = x² + 4x + 4x + 16 = x² + 8x + 16.

Multiply out.

  1. 137.(x + 1)² =
  2. 138.(x + 4)² =
  3. 139.(x + 5)² =
  4. 140.(x − 2)² =
  5. 141.(x − 3)² =
  6. 142.(x + 7)² =
  7. 143.(x − 4)² =
  8. 144.(x + 8)² =
  9. 145.(x − 5)² =
  10. 146.(x + 9)² =
  11. 147.(x + 11)² =
  12. 148.(x − 8)² =
  13. 149.(x + 12)² =
  14. 150.(x − 9)² =
  15. 151.(x + 13)² =
  16. 152.(x − 10)² =
  17. 153.(x + 14)² =
  18. 154.(x − 13)² =

8.A number in front of the x

Nothing new — still every term times every term. There is just a coefficient to carry through the first two multiplications.

Example(2x + 3)(x + 4) = 2x² + 8x + 3x + 12 = 2x² + 11x + 12.

Multiply out.

  1. 155.(2x + 1)(x + 3) =
  2. 156.(3x + 1)(x + 3) =
  3. 157.(3x + 4)(x + 2) =
  4. 158.(4x + 2)(x + 4) =
  5. 159.(5x + 5)(x + 5) =
  6. 160.(4x + 6)(x + 1) =
  7. 161.(2x − 1)(x + 3) =
  8. 162.(3x + 2)(x − 2) =
  9. 163.(3x + 7)(x + 8) =
  10. 164.(5x − 5)(x + 2) =
  11. 165.(3x + 7)(x + 9) =
  12. 166.(5x + 1)(x − 6) =
  13. 167.(5x + 4)(x − 6) =
  14. 168.(3x − 2)(x − 3) =
  15. 169.(5x − 1)(x + 7) =
  16. 170.(5x − 4)(x + 7) =
  17. 171.(5x − 7)(x + 5) =
  18. 172.(3x − 5)(x − 2) =
  19. 173.(2x − 4)(x + 9) =
  20. 174.(2x − 6)(x − 6) =
  21. 175.(2x − 7)(x − 4) =
  22. 176.(4x − 7)(x − 2) =

Part Two

Factoring

Now the same work backward. You are given what the multiplication produced and asked which binomials it came from. Everything here can be checked by multiplying your answer back out, and you should do that every single time — it is the only part of algebra where you can check your own work completely.

9.Taking out a common factor

Ask first whether something is in every term — a number, a variable, or both. If it is, it comes out in front and what is left goes in the parentheses. This section asks for that step and no more. Sometimes what is left in the parentheses will factor further and sometimes it will not; either way, stop here. Section 14 is where you are asked to go on.

Example3x² + 12x = 3x(x + 4), because 3x is in both terms.

Factor by taking out what is common.

  1. 177.7x² + 14x + 14 =
  2. 178.3x² + 15x =
  3. 179.2x² + 14x + 16 =
  4. 180.3x² + 18x =
  5. 181.3x² + 12x + 24 =
  6. 182.3x² + 24x + 6 =
  7. 183.4x² + 32x =
  8. 184.3x² + 30x − 6 =
  9. 185.4x² + 36x =
  10. 186.4x² + 40x =
  11. 187.7x² + 42x =
  12. 188.8x² + 40x − 24 =
  13. 189.6x² + 54x =
  14. 190.7x² + 56x + 28 =
  15. 191.5x² + 60x =
  16. 192.7x² + 70x + 56 =
  17. 193.7x² + 70x =
  18. 194.6x² + 72x =
  19. 195.8x² + 80x =
  20. 196.8x² + 80x − 24 =
  21. 197.7x² + 84x + 14 =
  22. 198.9x² + 108x =

10.Both numbers positive

Find two numbers that multiply to the last number and add to the middle one. When both the last and the middle are positive, both numbers are positive.

Examplex² + 7x + 12: two numbers multiplying to 12 and adding to 7 are 3 and 4, so it is (x + 3)(x + 4).

Factor. Check each answer by multiplying it back out.

  1. 199.x² + 2x + 1 =
  2. 200.x² + 7x + 6 =
  3. 201.x² + 6x + 8 =
  4. 202.x² + 8x + 7 =
  5. 203.x² + 10x + 9 =
  6. 204.x² + 11x + 10 =
  7. 205.x² + 12x + 11 =
  8. 206.x² + 7x + 12 =
  9. 207.x² + 8x + 12 =
  10. 208.x² + 10x + 16 =
  11. 209.x² + 12x + 20 =
  12. 210.x² + 9x + 20 =
  13. 211.x² + 10x + 21 =
  14. 212.x² + 11x + 24 =
  15. 213.x² + 12x + 27 =
  16. 214.x² + 12x + 35 =
  17. 215.x² + 13x + 40 =
  18. 216.x² + 14x + 40 =
  19. 217.x² + 14x + 45 =
  20. 218.x² + 15x + 50 =
  21. 219.x² + 15x + 54 =
  22. 220.x² + 16x + 55 =
  23. 221.x² + 15x + 56 =
  24. 222.x² + 16x + 60 =
  25. 223.x² + 16x + 63 =
  26. 224.x² + 18x + 77 =
  27. 225.x² + 18x + 80 =
  28. 226.x² + 21x + 110 =

11.Both numbers negative

When the last number is positive but the middle one is negative, the two numbers are both negative — two negatives multiply to a positive and add to a negative.

Examplex² − 7x + 12 = (x − 3)(x − 4).

Factor.

  1. 227.x² − 2x + 1 =
  2. 228.x² − 4x + 4 =
  3. 229.x² − 6x + 8 =
  4. 230.x² − 8x + 7 =
  5. 231.x² − 11x + 10 =
  6. 232.x² − 12x + 11 =
  7. 233.x² − 8x + 15 =
  8. 234.x² − 8x + 16 =
  9. 235.x² − 11x + 18 =
  10. 236.x² − 9x + 20 =
  11. 237.x² − 10x + 24 =
  12. 238.x² − 10x + 25 =
  13. 239.x² − 12x + 27 =
  14. 240.x² − 12x + 32 =
  15. 241.x² − 14x + 33 =
  16. 242.x² − 12x + 36 =
  17. 243.x² − 13x + 36 =
  18. 244.x² − 13x + 42 =
  19. 245.x² − 15x + 44 =
  20. 246.x² − 14x + 45 =
  21. 247.x² − 16x + 60 =
  22. 248.x² − 16x + 64 =
  23. 249.x² − 17x + 66 =
  24. 250.x² − 20x + 99 =
  25. 251.x² − 20x + 100 =
  26. 252.x² − 21x + 110 =

12.One of each sign

When the last number is negative the two numbers have opposite signs. Look for a pair whose difference is the middle number, and give the minus to whichever one makes the middle term come out right.

Examplex² + 2x − 15: the pair 5 and 3 differ by 2, and 5 × (−3) = −15 with 5 + (−3) = 2, so it is (x + 5)(x − 3).

Factor.

  1. 253.x² − x − 2 =
  2. 254.x² + 5x − 6 =
  3. 255.x² + 4x − 12 =
  4. 256.x² − 3x − 10 =
  5. 257.x² + 5x − 14 =
  6. 258.x² − 10x − 11 =
  7. 259.x² + 3x − 18 =
  8. 260.x² − 6x − 16 =
  9. 261.x² + 8x − 20 =
  10. 262.x² + 5x − 24 =
  11. 263.x² − 4x − 21 =
  12. 264.x² − 2x − 24 =
  13. 265.x² + 7x − 30 =
  14. 266.x² + x − 30 =
  15. 267.x² + 8x − 33 =
  16. 268.x² − 7x − 30 =
  17. 269.x² − 2x − 35 =
  18. 270.x² − 5x − 36 =
  19. 271.x² + 3x − 40 =
  20. 272.x² + 6x − 40 =
  21. 273.x² − 3x − 40 =
  22. 274.x² − 6x − 40 =
  23. 275.x² − 4x − 45 =
  24. 276.x² + 6x − 55 =
  25. 277.x² + 4x − 60 =
  26. 278.x² − 2x − 63 =
  27. 279.x² − 3x − 70 =
  28. 280.x² − 2x − 80 =
  29. 281.x² + 3x − 88 =
  30. 282.x² + x − 110 =

13.A square minus a square

Two terms, no middle one, both of them squares, subtracted. Take the square root of each and write one binomial with a plus and one with a minus.

Examplex² − 49 = (x + 7)(x − 7).

Factor.

  1. 283.x² − 9 =
  2. 284.x² − 16 =
  3. 285.x² − 36 =
  4. 286.x² − 81 =
  5. 287.x² − 144 =
  6. 288.x² − 169 =
  7. 289.x² − 196 =
  8. 290.x² − 225 =
  9. 291.x² − 256 =
  10. 292.x² − 289 =
  11. 293.x² − 324 =
  12. 294.x² − 361 =
  13. 295.x² − 441 =
  14. 296.x² − 484 =
  15. 297.x² − 529 =
  16. 298.x² − 576 =
  17. 299.x² − 625 =
  18. 300.x² − 676 =
  19. 301.x² − 729 =
  20. 302.x² − 784 =

14.Common factor first, then the pair

Take out what is common before looking for a pair of numbers. What is left in the parentheses is easier than what you started with, and a question that says factor completely is asking for both steps.

Example2x² + 10x + 12 = 2(x² + 5x + 6) = 2(x + 2)(x + 3).

Factor completely.

  1. 303.2x² + 6x + 4 =
  2. 304.3x² − 6x + 3 =
  3. 305.2x² + 10x + 12 =
  4. 306.2x² + 10x − 12 =
  5. 307.2x² − 10x − 12 =
  6. 308.3x² − 18x + 15 =
  7. 309.3x² + 18x − 21 =
  8. 310.3x² − 21x + 30 =
  9. 311.3x² + 3x − 36 =
  10. 312.5x² + 30x + 40 =
  11. 313.5x² + 30x + 45 =
  12. 314.4x² − 12x − 40 =
  13. 315.4x² − 4x − 48 =
  14. 316.3x² − 9x − 54 =
  15. 317.5x² − 5x − 60 =
  16. 318.5x² − 25x − 70 =
  17. 319.4x² + 4x − 80 =
  18. 320.5x² + 45x + 90 =
  19. 321.3x² − 9x − 84 =
  20. 322.4x² − 8x − 96 =
  21. 323.3x² − 39x + 126 =
  22. 324.5x² + 55x + 140 =
  23. 325.4x² + 52x + 168 =
  24. 326.5x² − 245 =

Part Three

Both directions at once

Nothing new. This part only removes the labels, so that you have to decide for yourself which of the two jobs a question is asking for.

15.You decide which job

These are mixed. If you are given two binomials multiplied together, multiply them out. If you are given three terms with no parentheses, factor them. Deciding which is which is half of the work on a test, where nothing is sorted into sections for you.

ExampleBinomials multiply out; three terms factor back.

Multiply out or factor, whichever the question needs.

  1. 327.(x + 2)(x + 3) =
  2. 328.x² + 3x + 2 =
  3. 329.(x + 4)(x + 5) =
  4. 330.(x − 1)(x + 2) =
  5. 331.(x + 6)(x + 1) =
  6. 332.(x + 1)(x − 3) =
  7. 333.x² − 3x + 2 =
  8. 334.(x + 7)(x + 6) =
  9. 335.x² − 4 =
  10. 336.(x − 1)(x − 1) =
  11. 337.(x + 9)(x + 4) =
  12. 338.(x − 1)(x + 6) =
  13. 339.(x − 6)(x + 2) =
  14. 340.(x − 7)(x + 6) =
  15. 341.(x + 3)(x − 7) =
  16. 342.(x + 7)(x − 3) =
  17. 343.(x + 8)(x − 4) =
  18. 344.x² + 2x − 8 =
  19. 345.(x − 2)(x − 5) =
  20. 346.(x − 5)(x − 2) =
  21. 347.(x − 5)(x − 5) =
  22. 348.(x − 9)(x + 9) =
  23. 349.(x + 1)(x − 9) =
  24. 350.(x − 6)(x − 6) =
  25. 351.x² + 9x + 14 =
  26. 352.(x − 7)(x − 8) =
  27. 353.(x − 8)(x − 9) =
  28. 354.x² + 9x + 18 =
  29. 355.x² − 5x − 14 =
  30. 356.x² − 3x − 18 =
  31. 357.x² − 11x + 24 =
  32. 358.x² + 11x + 30 =
  33. 359.x² + 3x − 28 =
  34. 360.x² − 6x − 27 =
  35. 361.x² + x − 42 =
  36. 362.x² + 4x − 45 =
  37. 363.x² + 2x − 48 =
  38. 364.x² − 15x + 54 =
  39. 365.x² + 3x − 54 =
  40. 366.x² − 18x + 81 =

Answer Key

Check your answers here. Every answer is written with the highest power first. For the factoring sections, the order of the two binomials does not matter — (x + 3)(x + 5) and (x + 5)(x + 3) are the same answer.

1.One number times parentheses (1–18)

  1. 1.2x + 4
  2. 2.6x + 12
  3. 3.6x + 24
  4. 4.6x + 42
  5. 5.4x − 12
  6. 6.3x + 24
  7. 7.6x + 54
  8. 8.2x + 20
  9. 9.5x + 50
  10. 10.8x + 80
  11. 11.9x + 90
  12. 12.5x + 55
  13. 13.9x + 108
  14. 14.3x − 27
  15. 15.9x − 63
  16. 16.4x − 40
  17. 17.9x − 90
  18. 18.2x − 22

2.A variable times parentheses (19–34)

  1. 19.2x² + 4x
  2. 20.2x² + 8x
  3. 21.2x² + 10x
  4. 22.5x² + 15x
  5. 23.6x² + 30x
  6. 24.3x² − 6x
  7. 25.4x² − 8x
  8. 26.4x² − 12x
  9. 27.4x² + 32x
  10. 28.5x² + 40x
  11. 29.2x² − 10x
  12. 30.3x² − 15x
  13. 31.5x² + 45x
  14. 32.2x² − 12x
  15. 33.6x² − 30x
  16. 34.5x² − 40x

3.Two binomials, both signs plus (35–64)

  1. 35.x² + 2x + 1
  2. 36.x² + 3x + 2
  3. 37.x² + 4x + 4
  4. 38.x² + 5x + 6
  5. 39.x² + 6x + 9
  6. 40.x² + 7x + 12
  7. 41.x² + 8x + 16
  8. 42.x² + 7x + 10
  9. 43.x² + 8x + 15
  10. 44.x² + 6x + 5
  11. 45.x² + 9x + 20
  12. 46.x² + 7x + 6
  13. 47.x² + 9x + 18
  14. 48.x² + 11x + 30
  15. 49.x² + 10x + 21
  16. 50.x² + 11x + 28
  17. 51.x² + 12x + 35
  18. 52.x² + 8x + 7
  19. 53.x² + 9x + 14
  20. 54.x² + 12x + 35
  21. 55.x² + 11x + 24
  22. 56.x² + 14x + 48
  23. 57.x² + 15x + 56
  24. 58.x² + 10x + 16
  25. 59.x² + 12x + 32
  26. 60.x² + 10x + 9
  27. 61.x² + 12x + 27
  28. 62.x² + 14x + 45
  29. 63.x² + 15x + 54
  30. 64.x² + 17x + 72

4.Two binomials, one sign minus (65–94)

  1. 65.x² − x − 2
  2. 66.x² − 4
  3. 67.x² − x − 2
  4. 68.x² − 16
  5. 69.x² + 4x − 5
  6. 70.x² + 2x − 15
  7. 71.x² − 3x − 10
  8. 72.x² + x − 20
  9. 73.x² + 2x − 24
  10. 74.x² + x − 30
  11. 75.x² − 3x − 18
  12. 76.x² − 2x − 24
  13. 77.x² − x − 30
  14. 78.x² + 5x − 6
  15. 79.x² − 6x − 7
  16. 80.x² − x − 42
  17. 81.x² + 6x − 7
  18. 82.x² − 49
  19. 83.x² − 6x − 16
  20. 84.x² − 2x − 48
  21. 85.x² − 64
  22. 86.x² − 7x − 8
  23. 87.x² − 6x − 16
  24. 88.x² + 6x − 16
  25. 89.x² + 3x − 40
  26. 90.x² + 2x − 48
  27. 91.x² + 8x − 9
  28. 92.x² − 5x − 36
  29. 93.x² + 7x − 18
  30. 94.x² + 6x − 27

5.Two binomials, both signs minus (95–118)

  1. 95.x² − 3x + 2
  2. 96.x² − 3x + 2
  3. 97.x² − 6x + 8
  4. 98.x² − 7x + 12
  5. 99.x² − 5x + 4
  6. 100.x² − 7x + 12
  7. 101.x² − 6x + 5
  8. 102.x² − 6x + 5
  9. 103.x² − 8x + 15
  10. 104.x² − 11x + 30
  11. 105.x² − 9x + 14
  12. 106.x² − 10x + 21
  13. 107.x² − 10x + 21
  14. 108.x² − 11x + 28
  15. 109.x² − 9x + 8
  16. 110.x² − 12x + 32
  17. 111.x² − 10x + 16
  18. 112.x² − 12x + 32
  19. 113.x² − 14x + 48
  20. 114.x² − 16x + 64
  21. 115.x² − 10x + 9
  22. 116.x² − 12x + 27
  23. 117.x² − 15x + 54
  24. 118.x² − 18x + 81

6.The middle disappears (119–136)

  1. 119.x² − 4
  2. 120.x² − 9
  3. 121.x² − 16
  4. 122.x² − 25
  5. 123.x² − 64
  6. 124.x² − 81
  7. 125.x² − 100
  8. 126.x² − 121
  9. 127.x² − 144
  10. 128.x² − 169
  11. 129.x² − 196
  12. 130.x² − 256
  13. 131.x² − 324
  14. 132.x² − 361
  15. 133.x² − 400
  16. 134.x² − 484
  17. 135.x² − 576
  18. 136.x² − 625

7.Squaring a binomial (137–154)

  1. 137.x² + 2x + 1
  2. 138.x² + 8x + 16
  3. 139.x² + 10x + 25
  4. 140.x² − 4x + 4
  5. 141.x² − 6x + 9
  6. 142.x² + 14x + 49
  7. 143.x² − 8x + 16
  8. 144.x² + 16x + 64
  9. 145.x² − 10x + 25
  10. 146.x² + 18x + 81
  11. 147.x² + 22x + 121
  12. 148.x² − 16x + 64
  13. 149.x² + 24x + 144
  14. 150.x² − 18x + 81
  15. 151.x² + 26x + 169
  16. 152.x² − 20x + 100
  17. 153.x² + 28x + 196
  18. 154.x² − 26x + 169

8.A number in front of the x (155–176)

  1. 155.2x² + 7x + 3
  2. 156.3x² + 10x + 3
  3. 157.3x² + 10x + 8
  4. 158.4x² + 18x + 8
  5. 159.5x² + 30x + 25
  6. 160.4x² + 10x + 6
  7. 161.2x² + 5x − 3
  8. 162.3x² − 4x − 4
  9. 163.3x² + 31x + 56
  10. 164.5x² + 5x − 10
  11. 165.3x² + 34x + 63
  12. 166.5x² − 29x − 6
  13. 167.5x² − 26x − 24
  14. 168.3x² − 11x + 6
  15. 169.5x² + 34x − 7
  16. 170.5x² + 31x − 28
  17. 171.5x² + 18x − 35
  18. 172.3x² − 11x + 10
  19. 173.2x² + 14x − 36
  20. 174.2x² − 18x + 36
  21. 175.2x² − 15x + 28
  22. 176.4x² − 15x + 14

9.Taking out a common factor (177–198)

  1. 177.7(x² + 2x + 2)
  2. 178.3x(x + 5)
  3. 179.2(x² + 7x + 8)
  4. 180.3x(x + 6)
  5. 181.3(x² + 4x + 8)
  6. 182.3(x² + 8x + 2)
  7. 183.4x(x + 8)
  8. 184.3(x² + 10x − 2)
  9. 185.4x(x + 9)
  10. 186.4x(x + 10)
  11. 187.7x(x + 6)
  12. 188.8(x² + 5x − 3)
  13. 189.6x(x + 9)
  14. 190.7(x² + 8x + 4)
  15. 191.5x(x + 12)
  16. 192.7(x² + 10x + 8)
  17. 193.7x(x + 10)
  18. 194.6x(x + 12)
  19. 195.8x(x + 10)
  20. 196.8(x² + 10x − 3)
  21. 197.7(x² + 12x + 2)
  22. 198.9x(x + 12)

10.Both numbers positive (199–226)

  1. 199.(x + 1)(x + 1)
  2. 200.(x + 1)(x + 6)
  3. 201.(x + 2)(x + 4)
  4. 202.(x + 7)(x + 1)
  5. 203.(x + 1)(x + 9)
  6. 204.(x + 10)(x + 1)
  7. 205.(x + 1)(x + 11)
  8. 206.(x + 3)(x + 4)
  9. 207.(x + 2)(x + 6)
  10. 208.(x + 2)(x + 8)
  11. 209.(x + 10)(x + 2)
  12. 210.(x + 5)(x + 4)
  13. 211.(x + 3)(x + 7)
  14. 212.(x + 8)(x + 3)
  15. 213.(x + 9)(x + 3)
  16. 214.(x + 7)(x + 5)
  17. 215.(x + 5)(x + 8)
  18. 216.(x + 4)(x + 10)
  19. 217.(x + 9)(x + 5)
  20. 218.(x + 10)(x + 5)
  21. 219.(x + 6)(x + 9)
  22. 220.(x + 11)(x + 5)
  23. 221.(x + 7)(x + 8)
  24. 222.(x + 10)(x + 6)
  25. 223.(x + 9)(x + 7)
  26. 224.(x + 11)(x + 7)
  27. 225.(x + 8)(x + 10)
  28. 226.(x + 10)(x + 11)

11.Both numbers negative (227–252)

  1. 227.(x − 1)(x − 1)
  2. 228.(x − 2)(x − 2)
  3. 229.(x − 2)(x − 4)
  4. 230.(x − 7)(x − 1)
  5. 231.(x − 10)(x − 1)
  6. 232.(x − 1)(x − 11)
  7. 233.(x − 5)(x − 3)
  8. 234.(x − 4)(x − 4)
  9. 235.(x − 2)(x − 9)
  10. 236.(x − 5)(x − 4)
  11. 237.(x − 6)(x − 4)
  12. 238.(x − 5)(x − 5)
  13. 239.(x − 9)(x − 3)
  14. 240.(x − 4)(x − 8)
  15. 241.(x − 11)(x − 3)
  16. 242.(x − 6)(x − 6)
  17. 243.(x − 9)(x − 4)
  18. 244.(x − 7)(x − 6)
  19. 245.(x − 4)(x − 11)
  20. 246.(x − 5)(x − 9)
  21. 247.(x − 10)(x − 6)
  22. 248.(x − 8)(x − 8)
  23. 249.(x − 11)(x − 6)
  24. 250.(x − 9)(x − 11)
  25. 251.(x − 10)(x − 10)
  26. 252.(x − 10)(x − 11)

12.One of each sign (253–282)

  1. 253.(x − 2)(x + 1)
  2. 254.(x − 1)(x + 6)
  3. 255.(x + 6)(x − 2)
  4. 256.(x + 2)(x − 5)
  5. 257.(x + 7)(x − 2)
  6. 258.(x + 1)(x − 11)
  7. 259.(x + 6)(x − 3)
  8. 260.(x + 2)(x − 8)
  9. 261.(x − 2)(x + 10)
  10. 262.(x + 8)(x − 3)
  11. 263.(x + 3)(x − 7)
  12. 264.(x + 4)(x − 6)
  13. 265.(x − 3)(x + 10)
  14. 266.(x + 6)(x − 5)
  15. 267.(x − 3)(x + 11)
  16. 268.(x − 10)(x + 3)
  17. 269.(x + 5)(x − 7)
  18. 270.(x − 9)(x + 4)
  19. 271.(x + 8)(x − 5)
  20. 272.(x − 4)(x + 10)
  21. 273.(x + 5)(x − 8)
  22. 274.(x − 10)(x + 4)
  23. 275.(x − 9)(x + 5)
  24. 276.(x − 5)(x + 11)
  25. 277.(x − 6)(x + 10)
  26. 278.(x − 9)(x + 7)
  27. 279.(x + 7)(x − 10)
  28. 280.(x + 8)(x − 10)
  29. 281.(x − 8)(x + 11)
  30. 282.(x − 10)(x + 11)

13.A square minus a square (283–302)

  1. 283.(x + 3)(x − 3)
  2. 284.(x + 4)(x − 4)
  3. 285.(x + 6)(x − 6)
  4. 286.(x + 9)(x − 9)
  5. 287.(x + 12)(x − 12)
  6. 288.(x + 13)(x − 13)
  7. 289.(x + 14)(x − 14)
  8. 290.(x + 15)(x − 15)
  9. 291.(x + 16)(x − 16)
  10. 292.(x + 17)(x − 17)
  11. 293.(x + 18)(x − 18)
  12. 294.(x + 19)(x − 19)
  13. 295.(x + 21)(x − 21)
  14. 296.(x + 22)(x − 22)
  15. 297.(x + 23)(x − 23)
  16. 298.(x + 24)(x − 24)
  17. 299.(x + 25)(x − 25)
  18. 300.(x + 26)(x − 26)
  19. 301.(x + 27)(x − 27)
  20. 302.(x + 28)(x − 28)

14.Common factor first, then the pair (303–326)

  1. 303.2(x + 2)(x + 1)
  2. 304.3(x − 1)(x − 1)
  3. 305.2(x + 3)(x + 2)
  4. 306.2(x + 6)(x − 1)
  5. 307.2(x − 6)(x + 1)
  6. 308.3(x − 1)(x − 5)
  7. 309.3(x + 7)(x − 1)
  8. 310.3(x − 2)(x − 5)
  9. 311.3(x + 4)(x − 3)
  10. 312.5(x + 4)(x + 2)
  11. 313.5(x + 3)(x + 3)
  12. 314.4(x + 2)(x − 5)
  13. 315.4(x − 4)(x + 3)
  14. 316.3(x + 3)(x − 6)
  15. 317.5(x − 4)(x + 3)
  16. 318.5(x + 2)(x − 7)
  17. 319.4(x + 5)(x − 4)
  18. 320.5(x + 6)(x + 3)
  19. 321.3(x + 4)(x − 7)
  20. 322.4(x + 4)(x − 6)
  21. 323.3(x − 7)(x − 6)
  22. 324.5(x + 7)(x + 4)
  23. 325.4(x + 6)(x + 7)
  24. 326.5(x − 7)(x + 7)

15.You decide which job (327–366)

  1. 327.x² + 5x + 6
  2. 328.(x + 1)(x + 2)
  3. 329.x² + 9x + 20
  4. 330.x² + x − 2
  5. 331.x² + 7x + 6
  6. 332.x² − 2x − 3
  7. 333.(x − 2)(x − 1)
  8. 334.x² + 13x + 42
  9. 335.(x + 2)(x − 2)
  10. 336.x² − 2x + 1
  11. 337.x² + 13x + 36
  12. 338.x² + 5x − 6
  13. 339.x² − 4x − 12
  14. 340.x² − x − 42
  15. 341.x² − 4x − 21
  16. 342.x² + 4x − 21
  17. 343.x² + 4x − 32
  18. 344.(x − 2)(x + 4)
  19. 345.x² − 7x + 10
  20. 346.x² − 7x + 10
  21. 347.x² − 10x + 25
  22. 348.x² − 81
  23. 349.x² − 8x − 9
  24. 350.x² − 12x + 36
  25. 351.(x + 7)(x + 2)
  26. 352.x² − 15x + 56
  27. 353.x² − 17x + 72
  28. 354.(x + 6)(x + 3)
  29. 355.(x − 7)(x + 2)
  30. 356.(x − 6)(x + 3)
  31. 357.(x − 3)(x − 8)
  32. 358.(x + 5)(x + 6)
  33. 359.(x − 4)(x + 7)
  34. 360.(x + 3)(x − 9)
  35. 361.(x − 6)(x + 7)
  36. 362.(x + 9)(x − 5)
  37. 363.(x − 6)(x + 8)
  38. 364.(x − 9)(x − 6)
  39. 365.(x − 6)(x + 9)
  40. 366.(x − 9)(x − 9)