Question

X^(2)+17x+72 im confused on how to factor this?

Answer 1

Answer:

  (x +9)(x +8)

Step-by-step explanation:

In a quadratic with leading coefficient 1, the coefficient of the linear term (17) is the sum of factors of the constant term (72). If you know your times tables, you know that 8×9 = 72, and you also know that 8+9 = 17.

With these facts, you can write the factorization as ...

  (x +8)(x +9)

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If you need to see the working out, rather than jumping to the end, you can use the sum information to rewrite the linear term:

  x^2 +(8x +9x) +72

Now factor pairs of terms:

  (x^2 +8x) + (9x +72) = x(x +8) +9(x +8) = (x +9)(x +8)

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It also helps to be familiar with the product of binomials:

  (x +a)(x +b) = x^2 +(a+b)x +ab