5 Section 5 Dividing Polynomials

Section 5.5 Objectives 1 Divide a Polynomial by a Monomial 2 Divide a Polynomial by a Binomial

Dividing by a Monomial Example: Divide and simplify: Use the quotient rule. Example: Divide and simplify: Use the quotient rule.

Dividing Polynomials Using Long Division Example: Divide: 1. Divide the highest term of the dividend, c2, by the first term of the divisor, c. 2. Multiply c by c + 1. 3. Subtract c2 + c from c2 + 3c – 2. Continued.

Dividing Polynomials Using Long Division Example continued: Bring down the next term to obtain a new polynomial. 2 c 4. Repeat the process until the degree of the remainder is less than the degree of the binomial divisor. Remainder 5. Check by verifying that (Quotient)(Divisor) + Remainder = Dividend. 

Dividing Polynomials Using Long Division Example: Divide: (y2 – 5y + 6) ÷ (y – 2) y – 3 y2 – 2y – 3y + 6 – 3y + 6 No remainder Check : (y – 2)(y – 3) = y2 – 5y + 6  Therefore, (y2 – 5y + 6) ÷ (y – 2) = y – 3