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f(x)=x^(3)-4x^(2)+3x-12
The function
f is shown. If
x-4 is a factor of
f, what is the value of
f(4) ?
Choose 1 answer:
(A) -12
(B) 0
(C) 12
(D) 64

The function $f$ is shown. If $x-4$ is a factor of $f$ , what is the value of $f(4)$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $-12$ $\newline$ (B) $0$ $\newline$ (C) $12$ $\newline$ (D) $64$

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Complex conjugate theorem

Full solution

Q. The function

f

is shown. If

x-4

is a factor of

f

, what is the value of

f(4)

?

\newline

Choose

1

answer:

\newline

(A)

-12

\newline

(B)

0

\newline

(C)

12

\newline

(D)

64

Verify Factor Theorem: If $x-4$ is a factor of $f(x)$ , then by the Factor Theorem, $f(4)$ should be equal to $0$ . Let's calculate $f(4)$ to verify this.
Substitute $x = 4$ : Substitute $x = 4$ into the polynomial $f(x) = x^3 - 4x^2 + 3x - 12$ . $\newline$ $f(4) = (4)^3 - 4\cdot(4)^2 + 3\cdot(4) - 12$
Calculate $f(4)$ : Calculate the value of $f(4)$ .
$f(4) = 64 - 4 \times 16 + 3 \times 4 - 12$
$f(4) = 64 - 64 + 12 - 12$
Simplify Expression: Simplify the expression to find the value of $f(4)$ . $f(4) = 0$

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