Polynomial long division divides one polynomial by another, term by term — exactly like the long division you use with numbers. You repeatedly divide the leading terms, multiply the divisor back, subtract, and bring down the next term, until nothing is left to divide. It is the reverse of multiplying polynomials.

Take x^2 + 5x + 6 divided by x + 2:

The answer is called the quotient. Here the division comes out exactly — there is no remainder — which means x + 2 is a factor. This is the same answer you would get by factorising x^2 + 5x + 6 = (x + 2)(x + 3) and cancelling the (x + 2).

See it built

Step through the long division of x^2 + 5x + 6 by x + 2: divide the leading terms, multiply the divisor back, subtract, bring down the next term, and repeat.

See it explained

Sal Khan works through dividing a polynomial by a linear expression using long division.