Technical Mathematics, Sixth Edition

2.11. Dividing a Polynomial by a Polynomial

Our final basic operation for this chapter is to divide an expression with two or more terms by another having two or more terms.

To divide one polynomial by another polynomial, follow these steps:

1. Write the divisor and the dividend in the order of descending powers of the variable.

2. Supply any missing terms, using coefficients of zero.

3. Set up the division in long-division form, as in the following example.

Note that this method is used only for polynomials, expressions in which the exponents are all positive integers.

Example 90: Divide (4x + x2 + 3) by (x + 1). Solution: Write the dividend in descending order of the powers. x2 + 4x + 3 There are no missing terms, so we go on to the next step. Set up in long-division format, making sure that the divisor is written in descending order of the powers as well. Divide the first term in the dividend (x2) by the first term in the divisor (x). The result (x) is written above the dividend, in line with the term having the same power. It is the first term of the quotient. Multiply the divisor by the first term of the quotient. Write the result below the dividend. Subtract it from the dividend. Repeat steps ...