# Polynomial Long Division – Exercise 5668

## Exercise

Do long division:

$$\frac{2x^9-7x^8+6x^7-25x^6+24x^5+14x^4-19x^3-20x^2+70}{24x^4-7x^3+10}$$

$$x^5+3x^3-2x^2+7$$

## Solution

Here is the long division:

This is the result of the long division:

$$\frac{2x^9-7x^8+6x^7-25x^6+24x^5+14x^4-19x^3-20x^2+70}{24x^4-7x^3+10}=$$

$$x^5+3x^3-2x^2+7$$

We can also present it like this:

$$2x^9-7x^8+6x^7-25x^6+24x^5+14x^4-19x^3-20x^2+70=$$

$$=(24x^4-7x^3+10)(x^5+3x^3-2x^2+7)$$

Note: it is exact division with no remainder.

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