Section 5.6 Dividing Polynomials

Dividing a Polynomial by a Monomial Divide each term of the polynomial by the monomial. When dividing variables, use the property

Example Divide. 3

Dividing a Polynomial by a Binomial Place the terms of the polynomial and binomial in descending order. Insert a 0 for any missing term. Divide the first term of the polynomial by the first term of the binomial. The result is the first term of the answer. Multiply the first term of the answer by the binomial and subtract the result from the first two terms of the polynomial. Bring down the next term to obtain a new polynomial. Divide the new polynomial by the binomial using the process described in step 2. Continue dividing, multiplying, and subtracting until the degree of the remainder is less than the degree of the binomial divisor. Write the remainder as the numerator of a fraction that has the binomial divisor as its denominator.

Example Divide. (c2 + 3c – 2) ÷ (c +1) Divide the first term of the polynomial by the first term of the binomial. Multiply the first term of the answer by the binomial. Subtract the result from the first two terms of the polynomial. Continued 5

Example (cont) Divide. (c2 + 3c – 2) ÷ (c +1) Bring down the next term to obtain a new polynomial. Repeat the process until the degree of the remainder is less than the degree of the binomial divisor. Remainder Write the remainder as the numerator of a fraction that has the binomial divisor as the denominator. 6

Example Divide. (y2 – 5y + 6) ÷ (y – 2) – 3 y2 – 2y – 3y + 6 – 3y + 6 No remainder (y2 – 5y + 6) ÷ (y – 2) = y – 3 Check : (y – 2) × (y – 3) = y2 – 5y + 6  7