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Select the correct answer.
if p(4) = -16, p(-6) = 0, and P(5) P(-6), which statement must be true?
A. (x + 16) is a factor of p.
B. (x + 4) is a factor of p.
C. (x + 6) is a factor of p.
D. (x – 5) is a factor of p.

Respuesta :

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)".

kapoorprachi783

(x+6) is a factor of p.

The answer is option C.

How to solve the function?

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)".

Learn more about function here: https://brainly.com/question/4025726

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