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Polynomial Long Division – Exercise 5658

Exercise

Do long division:

\frac{3x^5+2x^3-5x+6}{x^2-x+3}

Final Answer


(3x^3+3x^2-4x-13)+\frac{-6x+45}{x^2-x+3}

Solution

Here is the long division:

This is the result of the long division:

\frac{3x^5+2x^3-5x+6}{x^2-x+3}=

=(3x^3+3x^2-4x-13)+\frac{-6x+45}{x^2-x+3}

We can also present it like this:

3x^5+2x^3-5x+6=

=(x^2-x+3)(3x^3+3x^2-4x-13)+(-6x+45)

Note:

-6x+45 \text{ is called the remainder.}

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