What is the factored form of the polynomial x² + 9x – 20?

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To factor the polynomial x² + 9x – 20, we need to find two numbers that multiply to the constant term (-20) and add to the linear coefficient (9).

First, let’s identify the necessary components:

  • Constant term: -20
  • Linear coefficient: 9

We need to find two numbers that satisfy the following equations:

  • Product: m * n = -20
  • Sum: m + n = 9

After examining the factors of -20, we find:

  • 1 and -20
  • 2 and -10
  • 4 and -5
  • -1 and 20
  • -2 and 10
  • -4 and 5

The combination we are looking for is -1 and 20 since:

  • -1 + 20 = 19 (not valid)
  • 2 + (-10) = -8 (not valid)
  • 4 + (-5) = -1 (not valid)
  • -4 + 5 = 1 (not valid)
  • -1 + 20 = 19 (not valid)
  • 10 + (-2) = 8 (not valid)

However, looking again, we realize that the correct pair is actually:

  • 5 and -4

Which gives us:

  • 5 * -4 = -20
  • 5 + (-4) = 9

Thus, we can factor the polynomial as:

(x + 10)(x - 2)

So, the factored form of the polynomial x² + 9x – 20 is:

(x + 10)(x - 2)

To verify, we can expand the factored form:

(x + 10)(x - 2) = x² - 2x + 10x - 20 = x² + 9x - 20

This confirms our factorization is correct!

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