Find the quotient and remainder when $f(x)$ = $3x^3 − 2x^2 + 5x − 7$ is divided by $x + 2$.
I found quotient to be $3x^2 - 8x -11$ with remainder 15. I'm sure the remainder is correct but not sure about the quotient, am I right?
Finding quotient and remainder
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algebra-precalculus
proof-verification
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0Is it hard to check? – 2017-01-11
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0You should check the step where a $-8x^2+5x$ appears. I believe a sign error occurred there. – 2017-01-11
2 Answers
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When you factor polynomials like this over, you should end up with \begin{equation*} f(x)=p(x)(x+2)+r(x) \end{equation*} Where $r(x)$ is a polynomial with degree less than $deg(x+2)$. In this case that gives you a constant. This allows you to plug in $-2$ for $x$ to discover the remainder!
\begin{equation*} f(-2)=-49 \end{equation*}
It looks like you need to tweak your remainder. Have you heard of synthetic division? This video might help:
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By definition of the remainder and the quotient, if you are right you should have $$ 3x^3 - 2x^2 + 5x - 7 = (3x^2 -8x - 11)(x + 2) + 15. $$ Do you?