Consider the following. P(x) = x^3 + 2x^2 − 16x − 32, c = −2 Find all other zeros of P(x). (Enter your answers as a comma-separated list. Enter all answers including repetitions.) x =

Question

i already tried -2,-4,4

Answer 1

What you say you tried are the right answers. I was going to say to use synthetic division with -2, but this is an easy division to do. Notice how x+2 clearly divides the first two and last two terms:

x²(x+2) = x³ + 2x²

-16(x+2) = -16x - 32

Thus, x³ + 2x² -16x - 32 = (x² - 16)(x + 2) = (x - 4)(x + 4)(x + 2)

The other zeroes are -4, 4