# Polynomial Long Division – Exercise 5664

## Exercise

Do long division:

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

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

## Solution

Here is the long division:

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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