Question

Select the correct answer.

Answer 1

Answer: C. (x+6) is a factor of p

Explanation:

p(-6) = 0 means that plugging x = -6 into p(x) leads to p(x) = 0.

If (x+6) was a factor of p(x), then we can say

p(x) = (x+6)q(x)

where q(x) is some other polynomial. Now let's replace x with -6

p(x) = (x+6)q(x)

p(-6) = (-6+6)q(-6)

p(-6) = 0*q(-6)

p(-6) = 0

The value of q(-6) doesn't matter as multiplying 0 with any number leads to 0.

This is all based on the special case of the remainder theorem that says "if p(k) = 0, then (x-k) is a factor of p(x)".