Question

Express h(x) as a product of two factors-

h(x)=x−4x3−2x2−16x−32
A. (x−8)(x+4)
B. (x−4)(x+8)
C. (x+4)(x−8)
D. (x+8)(x−4)

Answer 1

To express h(x) as a product of two factors, factor pairs of the constant term are examined to find a pair that adds to the coefficient of the x term. The correct answer is (x + 4)(x - 8), corresponding to option C.

Step-by-step explanation:

To express the function h(x) = x - 4x^3 - 2x^2 - 16x - 32 as a product of two factors, we need to find factors of the constant term (-32) that when added give us the coefficient of the x term (which is -16). Let's look at the options given:

• (x - 8)(x + 4)
• (x - 4)(x + 8)
• (x + 4)(x - 8)
• (x + 8)(x - 4)

Factor pairs of -32 are (-32, 1), (-16, 2), (-8, 4), (-4, 8), (32, -1), (16, -2), (8, -4), (4, -8). We need the pair that adds up to -16. The correct pair is (4, -8), which means the correct factorization is (x + 4)(x - 8), which corresponds to option C.