1. Polynomials and Polynomial Functions
*Chapter 5
Polynomials and Polynomial Functions

2. Chapter Sections 5.1 – Addition and Subtraction of Polynomials
5.2 – Multiplication of Polynomials
5.3 – Division of Polynomials and Synthetic Division
5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping
5.5 – Factoring Trinomials
5.6 – Special Factoring Formulas
5.7-A General Review of Factoring
5.8 - Polynomial Equations
Chapter 1 Outline

3. Recall: Special Products:
(a + b)2 = (a + b)(a + b) = a2 + 2ab + b2
(a – b)2 = (a – b)(a – b) = a2 – 2ab + b2
(a + b)(a – b) = a2 – b2

4. Division of Polynomials and Synthetic Division
§ 5.3
Division of Polynomials and Synthetic Division
Objectives:
Divide a Polynomial by a Monomial
Divide a Polynomial by a binomials.
Divide a Polynomial by a polynomials.

5. Divide a Monomial by a Monomial: Use the quotient rule for exponents
Example 1

6. Divide a Polynomial by a Monomial: Example 2
Solution
Divide each term in the polynomial by the monomial.

7. To divide a polynomial by a polynomial, use the same method as when performing long division.
Example 3
Divide.
Solution Begin by dividing the first term in the dividend, x2 + 8x + 16 by the first term in the divisor: x + 3.
Change signs.
Answer
Change signs.

8. Example 4 :
Answer

9. Solution Begin by dividing the first term in the dividend by the first term in the divisor: 6b2 + 5b – 28.
Example 5
Change signs.
Answer
Change signs.

10. The Remainder Theorem Remainder Theorem
If the polynomial P(x) is divided by x – a, the remainder is equal to P(a).

11. Dividing Polynomials
To divide a polynomial by a polynomial, use the same method as when performing long division.
dividend
divisor
1. Divide 6t 2 by 2t. Write the quotient above the term containing the t. 3t
- 8
-16t  2t = - 8
2. Multiply the 3t by 2t Write the product under the like terms.
6t2 + 15t
3. Subtract. Bring down the remaining term.
-16t - 40
-16t - 40
4. Repeat, using the first term in the bottom row:
-16t - 40
Check your answer using the FOIL method.