Answer:
"The number c is a <u>zero</u> the polynomial function y=P(x) if and only if x-c is a <u>factor</u> of the polynomial P(x)."
Step-by-step 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 <em>root (zero or solution)</em> 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 <u>zero</u> the polynomial function y=P(x) if and only if x-c is a <u>factor</u> of the polynomial P(x)."