# How do you divide (2x^3-x+1)div(x^2+x+1) using synthetic division?

Jan 17, 2018

$\textcolor{b l u e}{\frac{2 {x}^{3} - x + 1}{{x}^{2} + x + 1} = 2 x - 2 + \frac{- x + 3}{{x}^{2} + x + 1}}$

#### Explanation:

Synthetic Division is used to divide polynomials by binomials of the form color(green)((x-a)

Polynomial Long Division Method is used to divide polynomials by other polynomials

Hence, Polynomial Long Division Method is used to provide a solution for the given problem.

We will now perform the Polynomial Long Division using

Hence, the Quotient = $2 x - 2$

Remainder = $\left(- x + 3\right)$

Hence, the Result of our Long Polynomial Division is

color(blue)(2x -2 + (-x+3)/(x^2+x+1)

Hope you find this solution useful.