# How do I divide polynomials by using long division?

Dec 20, 2015

Here's an example, dividing ${x}^{3} + {x}^{2} - x - 1$ by $x - 1$ ...

#### Explanation:

Long division of polynomials is similar to long division of numbers...

Write the dividend under the bar and the divisor to the left of the bar.

Start writing the quotient above the bar, choosing the first term $\textcolor{b l u e}{{x}^{2}}$ so that when multiplied by the divisor the leading term of the product matches the leading term of the dividend.

Then write the product of the first term by the divisor under the dividend and subtract it to get a remainder $2 {x}^{2}$.

Bring down the next term from the dividend alongside it to form your running remainder $2 {x}^{2} - x$.

Then choose the next term $\textcolor{b l u e}{2 x}$ for the quotient, so that when multiplied by the divisor it matches the leading term of the running remainder.

Write the product under the remainder and subtract to get the next remainder, etc.

Repeat until the running remainder is of lower degree than the divisor and there are no more terms to bring down from the dividend.

In this particular example, the division is exact, so you are left with no remainder at the end.