f(x)=2x^5+x^4-18x^3-17x^2+20x+12 The function f is shown. If x - 3 is a factor of f , what is the value of f(3)?

Understand Relationship: Understand the relationship between factors and function values. If x - 3 is a factor of the function f(x), then f(3) must be equal to 0, because when x = 3, the factor x - 3 becomes zero, and anything multiplied by zero is zero.Substitute x = 3: Substitute x = 3 into the function f(x) to find f(3). f(x) = 2x^5 + x^4 - 18x^3 - 17x^2 + 20x + 12 f(3) = 2(3)^5 + (3)^4 - 18(3)^3 - 17(3)^2 + 20(3) + 12Calculate f(3): Calculate the value of f(3). f(3) = 2(243) + (81) - 18(27) - 17(9) + 20(3) + 12 f(3) = 486 + 81 - 486 - 153 + 60 + 12Simplify Expression: Simplify the expression to find the final value of f(3). f(3) = 486 + 81 - 486 - 153 + 60 + 12 f(3) = 0 + 81 - 153 + 60 + 12 f(3) = 81 - 153 + 60 + 12 f(3) = -72 + 60 + 12 f(3) = -12 + 12 f(3) = 0

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The function $f(x) = 2x^5 + x^4 - 18x^3 - 17x^2 + 20x + 12$ is shown. If $x - 3$ is a factor of $f$ , what is the value of $f(3)$ ?

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Q. The function

f(x) = 2x^5 + x^4 - 18x^3 - 17x^2 + 20x + 12

is shown. If

x - 3

is a factor of

f

, what is the value of

f(3)

Understand Relationship: Understand the relationship between factors and function values. $\newline$ If $x - 3$ is a factor of the function $f(x)$ , then $f(3)$ must be equal to $0$ , because when $x = 3$ , the factor $x - 3$ becomes zero, and anything multiplied by zero is zero.
Substitute $x = 3$ : Substitute $x = 3$ into the function $f(x)$ to find $f(3)$ .
$f(x) = 2x^5 + x^4 - 18x^3 - 17x^2 + 20x + 12$
$f(3) = 2(3)^5 + (3)^4 - 18(3)^3 - 17(3)^2 + 20(3) + 12$
Calculate $f(3)$ : Calculate the value of $f(3)$ .
$f(3) = 2(243) + (81) - 18(27) - 17(9) + 20(3) + 12$
$f(3) = 486 + 81 - 486 - 153 + 60 + 12$
Simplify Expression: Simplify the expression to find the final value of $f(3)$ . $f(3) = 486 + 81 - 486 - 153 + 60 + 12$ $f(3) = 0 + 81 - 153 + 60 + 12$ $f(3) = 81 - 153 + 60 + 12$ $f(3) = -72 + 60 + 12$ $f(3) = -12 + 12$ $f(3) = 0$