Dividing Polynomials by Binomials With Example

Dividing a polynomial by a binomial means sharing the polynomial's terms between the two parts of the divisor. The most reliable school method is polynomial long division, done one term at a time.

The method, in order

1. Arrange both polynomials in descending powers of x. 2. Divide the first term of the dividend by the first term of the divisor. 3. Multiply the whole divisor by that result and subtract. 4. Bring down the next term and repeat until the remaining degree is smaller than the divisor's degree.

Worked example

Divide x² + 5x + 6 by (x + 2).

x² ÷ x = x. Multiply: x(x + 2) = x² + 2x. Subtract: (x² + 5x) − (x² + 2x) = 3x. Bring down 6. Then 3x ÷ x = 3. Multiply: 3(x + 2) = 3x + 6. Subtract and you get 0.

Answer: The quotient is x + 3, with remainder 0, so (x + 2) is a factor.

Check your answer

Multiply the quotient by the divisor and add the remainder. You should get back the original polynomial.

Learn more

For a video explanation of this topic, see Khan Academy Algebra course.

Dividing Polynomials by Binomials With Example

The method, in order

Worked example

Check your answer

Learn more

Related guides