Worked examples
Two examples
Example 1
Factor: 2x2 + 7x + 3
- The first terms: 2x and x. The last numbers multiply to 3: 1 and 3.
- Try (2x + 1)(x + 3): outer 6x, inner x, together 7x. It works.
Answer: (2x + 1)(x + 3)
Example 2
Factor: 3x2 − 10x + 8
- First terms 3x and x. Last numbers multiply to 8 and the middle is negative, so both are negative.
- Try (3x − 4)(x − 2): −6x and −4x make −10x.
Answer: (3x − 4)(x − 2)
Where this is taught: Quiz 39: Polynomials and Factoring, “The signs, which is where the thinking is”
The drill
Ten problems
How many:
Type your answer as a product, like (x + 2)(x - 3). Then press Check my answers at the bottom.Write each answer on the line. The answer key, with the reasoning, is on the last page.