When attempting to find the roots of a polynomial, it will be useful to be able to divide that polynomial by other polynomials. Here we'll learn how.

Long division of polynomials is a lot like long division of real numbers. If the polynomials involved were written in fraction form, the numerator would be the dividend, and the denominator would be the divisor. To divide polynomials using long division, first divide the first term of the dividend by the first term of the divisor. This is the first term of the quotient. Multiply the new term by the divisor, and subtract this product from the dividend. This difference is the new dividend. Repeat these steps, using the difference as the new dividend until the first term of the divisor is of a greater degree than the new dividend. The last "new dividend" whose degree is less than that of the divisor is the remainder. If the remainder is zero, the divisor divided evenly into the dividend. In the example below, f (x) = x4 +4x3 + x - 10 is divided by g(x) = x2 + 3x - 5.