Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

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

View step-by-step help

View step-by-step help

Full solution

Q.

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

\newline

The function

f

is shown. If

x-3

is a factor of

f

, what is the value of

f(3)

Given Factor Theorem: We are given that $x-3$ is a factor of the function $f(x)$ . According to the Factor Theorem, if $x-3$ is a factor of $f(x)$ , then $f(3)$ must be equal to $0$ .
Substitute $x$ with $3$ : To find the value of $f(3)$ , we substitute $x$ with $3$ in the function $f(x)$ . $f(3) = 2(3)^5 + (3)^4 - 18(3)^3 - 17(3)^2 + 20(3) + 12$
Calculate $f(3)$ : Now, we calculate the value of $f(3)$ step by step. $\newline$ $f(3) = 2(243) + 81 - 18(27) - 17(9) + 60 + 12$
Continue Calculations: Continue with the calculations. $f(3) = 486 + 81 - 486 - 153 + 60 + 12$
Combine Like Terms: Combine like terms to find the value of $f(3)$ . $f(3) = 486 - 486 + 81 - 153 + 60 + 12$
Simplify Expression: Simplify the expression. $f(3) = 0 + 81 - 153 + 60 + 12$
Finish Calculation: Finish the calculation. $\newline$ $f(3) = 81 - 153 + 60 + 12$ $\newline$ $f(3) = -72 + 60 + 12$ $\newline$ $f(3) = -12 + 12$ $\newline$ $f(3) = 0$

More problems from Power rule

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 2 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 1 month ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 1 month ago

Question

\newline

32^{(-1/5)}

Posted 1 month ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 1 month ago