Polynomial Long Division – Exercise 5658

Exercise

Do long division:

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

Final Answer

Show final answer

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:

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