Question

The number c is a​ _______ of the polynomial function yequals=​P(x) if and only if xminus−c is a​ _______ of the polynomial​ P(x).

Answer 1

I am 86% sure that it is The number c is zero the polynomial function y=​P(x) if and only if x-c is a​ factor of the polynomial​ P(x)

Hope this helped!

Answer 2

"The number c is a​ zero the polynomial function y=​P(x) if and only if x-c is a​ factor of the polynomial​ P(x)."

Explanation:

We have been given some statements with blank spaces:

"The number c is a​ _______ of the polynomial function y=​P(x) if and only if x-c is a​ _______ of the polynomial​ P(x)."

Now we need to fill those blank spaces by suitable words.

We know that if x=5 is some root (zero or solution) of the polynomial function then (x-5) works as factor.

So using that logic, we can fill the blanks spaces as:

"The number c is a​ zero the polynomial function y=​P(x) if and only if x-c is a​ factor of the polynomial​ P(x)."