AskRose.org
Email a Tutor
Home > Student Resources > Dividing Polynomials

Dividing Polynomials

To divide polynomials, we divide the first term of the numerator by the first one in the denominator and then put that term into the answer. From there we multiply the denominator and put that answer below the numerator, and then finally subtract to create a new polynomial.

Example

Divide:

    \[3x^{3} + 5x^{2} - x + 2 \quad by \quad x + 2\]

    \[(x+2)\frac{3x^2 - x + 1}{\lvert3x^{3} + 5x^{2} - x + 2}\]

    \[\frac{-(3x^3 + 6x^2)}{0 - x^2 - x + 2}\]

    \[\frac{-\quad(-x^2 -2x)}{0 + x + 2}\]

    \[\frac{-\quad(x + 2)}{0\quad0}\]

    \[(3x^2)(x) = 3x^3 \]

    \[(3x^2)(x+2) = 3x^3 + 6x^2\]

    \[(-x)(x) = -x^2\]

    \[(-x)(x + 2) = -x^2 - 2x\]

    \[(1)(x + 2) = (x + 2)\]

\boxed{\frac{3x^{3} + 5x^{2} - x + 2}{x+1} = 3x^2 - x + 1}