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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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Solve quadratic inequalities

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

Understand Relationship and Value: Understand the relationship between factors of a polynomial and the value of the polynomial. $\newline$ 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 factor $(x - 9)$ gives us $0$ .
Apply Factor Theorem: Apply the Factor Theorem to find the value of $f(9)$ . $\newline$ The Factor Theorem states that if $(x - a)$ is a factor of a polynomial $f(x)$ , then $f(a) = 0$ . Since we are given that $(x - 9)$ is a factor of $f$ , we can set $a = 9$ and evaluate $f(9)$ .
Calculate $f(9)$ : Calculate $f(9)$ using the information that $(x - 9)$ is a factor of $f$ . $\newline$ $f(9) = 0$ because $(x - 9)$ is a factor of $f$ .

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