Polynomial Long Division

Polynomial Long Division

Polynomial long division works like numerical long division, but with terms in powers of a variable.

1) Arrange the polynomials

Write both polynomials in descending order of powers. If a power is missing, include it with coefficient 0. This helps keep the terms aligned.

2) Divide the leading terms

Divide the first term of the dividend by the first term of the divisor. That gives the next term of the quotient.

3) Multiply and subtract

Multiply the entire divisor by the new quotient term, then subtract the result from the current polynomial. Be careful with signs when subtracting.

4) Bring down the next term

After subtracting, bring down the next term from the dividend and repeat the process until the degree of the remainder is less than the degree of the divisor.

5) Write the answer clearly

Your result should be written as:

• quotient, plus
• remainder divided by the divisor, if there is a remainder.

Check your work

Multiply the divisor by your quotient, then add the remainder. If you recover the original dividend, your division is correct.