Polynomial Long Division – Exercise 5668

Exercise

Do long division:

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

Final Answer

Show final answer

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.