1. 5 Section 5
Dividing Polynomials

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

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

4. 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.

5. 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. 

6. 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