The correct factorization of 12x'2 - 157x - 40: A) (3x -8)(4x - 5) B) (3x - 40)(4x + 1) C) (12x - 1)(x + 40) D) (12x - 5)(x-8)

B

Step-by-step explanation:

12x² - 157x - 40

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 12 × - 40 = - 480 and sum = - 157

The factors are + 3 and - 160

Use these factors to split the x- term

12x² + 3x - 160x - 40 ( factor the first/second and third/fourth terms

= 3x(4x + 1) - 40(4x + 1) ← factor out (4x + 1) from each term

= (4x + 1)(3x - 40) ← in factored form → B

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.