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If
x-9 is a factor of the polynomial function
f, what is the value of
f(9) ?
Choose 1 answer:
(A) -9
(B) 0
(c) 9
(D) Cannot be determined from the given information

If $x-9$ is a factor of the polynomial function $f$ , what is the value of $f(9)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-9$ $\newline$ (B) $0$ $\newline$ (C) $9$ $\newline$ (D) Cannot be determined from the given information

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Descartes' Rule of Signs

Full solution

Q. If

x-9

is a factor of the polynomial function

f

, what is the value of

f(9)

?

\newline

Choose

1

answer:

\newline

(A)

-9

\newline

(B)

0

\newline

(C)

9

\newline

(D) Cannot be determined from the given information

Apply Factor Theorem: If $x-9$ is a factor of the polynomial function $f$ , then by the Factor Theorem, $f(9)$ must be equal to $0$ because plugging $x = 9$ into the function should yield a result of $0$ .
Substitute $x = 9$ : To find the value of $f(9)$ , we substitute $x = 9$ into the function $f$ . Since $x-9$ is a factor, $f(9) = 0\times(\text{anything}) = 0$ , where $\text{＂anything＂}$ represents the other factors of the polynomial.
Find $f(9)$ : Therefore, the value of $f(9)$ is $0$ , which corresponds to option (B).

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