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Factoring x² + bx + c

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The question

x² + 12x + 11

x² + 12x + 11

x² + 12x + 11
multiply to11· add to12
1·11
1·11
11and1
x² + 12x + 11=(x + 11)(x + 1)
  1. Factoring this means finding two numbers to put in (x + ▢)(x + ▢). They multiply to 11, the last term, and add to 12, the number in front of x.
  2. Now list the pairs that multiply to 11. There are only 1: 1 and 11.
  3. Which of them adds to 12? 11 × 1 = 11 and 11 + 1 = 12. So the two numbers are 11 and 1.
  4. Put them in the brackets: x² + 12x + 11 = (x + 11)(x + 1). Multiply back out to check.

How it works.

  1. 01

    Factoring this means finding two numbers to put in (x + ▢)(x + ▢). They multiply to 11, the last term, and add to 12, the number in front of x.

  2. 02

    Now list the pairs that multiply to 11. There are only 1: 1 and 11.

  3. 03

    Which of them adds to 12? 11 × 1 = 11 and 11 + 1 = 12. So the two numbers are 11 and 1.

  4. 04

    Put them in the brackets: x² + 12x + 11 = (x + 11)(x + 1). Multiply back out to check.

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