X^(2) + x - 72 Replace the values of a and b to rewrite the given expression. (x +a) (x + b)

Question

`x^(2) + x - 72`

Replace the values of a and b to rewrite the given expression.

`(x +a) (x + b)`

Answer 1

(x + 9)(x - 8)

Explanation:

x² + x - 72

consider the factors of the constant term (- 72) which sum to give the coefficient of the x- term (+ 1)

the factors are + 9 and - 8 , since

9 × - 8 = - 72 and + 9 - 8 = + 1

use these factors to split the x- term

x² + 9x - 8x - 72 ( factor the first/second and third/fourth terms )

= x(x + 9) - 8(x + 9) ← factor out (x + 9) from each term

= (x + 9)(x - 8) ← in factored form

with a = 9 and b = - 8