The following polynomial has factors (x + 8) and (3x + 2). Determine the value of k. −6x^3-55x^2+kx−16

Step-by-step explanation:

Since (x + 8) and (3x + 2) are factors of the polynomial it means that if either one of them is equated to zero and substituted into the polynomial will give us zero

Using x + 8

We have

x + 8 = 0

x = - 8

Substitute the value of x into the polynomial

- 6x³ - 55x² + kx - 16

That's

- 6(-8)³ - 55(-8)² + k(-8) - 16 = 0

-6(-512) - 55(64) - 8k - 16 = 0

Expand

3072 - 3520 - 8k - 16 = 0

Simplify

- 464 - 8k = 0

8k = -464

Divide both sides by 8

k = - 58

Hope this helps you

what i would say the best answer is a. 40.5