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f(x)=x^ $4$ + $4$ x^ $3$ $-7$ x^ $2$ $-22$ x+ $24$ The function f is shown. If x+ $3$ is a factor of f, what is the value of f( $-3$ )?

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Find derivatives using the quotient rule I

Full solution

Q. f(x)=x^

4

+

4

x^

3

-7

x^

2

-22

x+

24

The function f is shown. If x+

3

is a factor of f, what is the value of f(

-3

)?

Find f( $-3$ ): First, we need to find $f(-3)$ .
Substitute x = $-3$ : Substitute $x = -3$ into $f(x)$ : $\newline$ $f(-3) = (-3)^4 + 4(-3)^3 - 7(-3)^2 - 22(-3) + 24$
Calculate ( $-3$ )^ $4$ : Calculate $(-3)^4$ : $\newline$ $(-3)^4 = 81$
Calculate $4$ ( $-3$ )^ $3$ : Calculate $4(-3)^3$ : $\newline$ $4(-3)^3 = 4(-27) = -108$
Calculate $-7$ ( $-3$ )^ $2$ : Calculate $-7(-3)^2$ : $\newline$ $-7(-3)^2 = -7(9) = -63$
Calculate $-22$ ( $-3$ ): Calculate $-22(-3)$ : $\newline$ $-22(-3) = 66$
Add all terms: Add all the terms together: $\newline$ $f(-3) = 81 - 108 - 63 + 66 + 24$
Simplify expression: Simplify the expression: $\newline$ $f(-3) = 81 - 108 = -27$ $\newline$ $-27 - 63 = -90$ $\newline$ $-90 + 66 = -24$ $\newline$ $-24 + 24 = 0$

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