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The form of your answer should either be $p(x)$ or $p(x)+\frac{k}{x-5}$ where $p(x)$ is a polynomial and $k$ is an integer. $\frac{5x^3-22x^2-17x+11}{x-5}$

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Power rule with rational exponents

Full solution

Q. The form of your answer should either be

p(x)

or

p(x)+\frac{k}{x-5}

where

p(x)

is a polynomial and

k

is an integer.

\frac{5x^3-22x^2-17x+11}{x-5}

Divide Leading Terms: question_prompt: Simplify the expression $(5x^3-22x^2-17x+11)/(x-5)$ and write it in the form $p(x)$ or $p(x)+(k)/(x-5)$ .
Subtract Result: Use polynomial long division to divide $5x^3 - 22x^2 - 17x + 11$ by $x - 5$ .
Repeat Process: Divide the leading term of the dividend $5x^3$ by the leading term of the divisor $x$ to get $5x^2$ . Multiply $x - 5$ by $5x^2$ to get $5x^3 - 25x^2$ . Subtract this from the original polynomial to get $3x^2 - 17x + 11$ .
Divide Coefficients: Repeat the process: Divide $3x^2$ by $x$ to get $3x$ . Multiply $x - 5$ by $3x$ to get $3x^2 - 15x$ . Subtract this from $3x^2 - 17x + 11$ to get $-2x + 11$ .
Check Remainder: Divide $-2x$ by $x$ to get $-2$ . Multiply $x - 5$ by $-2$ to get $-2x + 10$ . Subtract this from $-2x + 11$ to get $1$ .
Check Remainder: Divide $-2x$ by $x$ to get $-2$ . Multiply $x - 5$ by $-2$ to get $-2x + 10$ . Subtract this from $-2x + 11$ to get $1$ . The remainder is $1$ , which is less than the degree of the divisor $(x - 5)$ . The division process is complete.

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