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Polynomial Long Division – Exercise 5664

Exercise

Do long division:

\frac{12x^5-3x^4+5x^3+x^2-7}{x^2-x-5}

Final Answer


(12x^3+9x^2+74x+120)+\frac{490x+593}{x^2-x-5}

Solution

Here is the long division:

long division 2

This is the result of the long division:

\frac{12x^5-3x^4+5x^3+x^2-7}{x^2-x-5}

=(12x^3+9x^2+74x+120)+\frac{490x+593}{x^2-x-5}

We can also present it like this:

12x^5-3x^4+5x^3+x^2-7=

=(x^2-x-5)(12x^3+9x^2+74x+120)+(490x+593)

Note:

490x+593 \text{ is called the remainder.}

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