1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1 Polynomials and Polynomial Functions Chapter 5

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – 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 Polynomial Equations Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3 § 5.3 Division of Polynomials and Synthetic Division

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4 Divide a Polynomial by a Monomial To Divide a Polynomial by a Monomial Divide each term of the polynomial. To divide a polynomial by a monomial, we will need to use the quotient rule for exponents, the zero exponent rule, and the negative exponent rule.

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5 Divide a Polynomial by a Monomial Example

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6 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. 3t3t 2. Multiply the 3t by 2t + 5. Write the product under the like terms. 6t t 3. Subtract. Bring down the remaining term. -16t - 40

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7 Dividing Polynomials 3t3t 6t 2 +15t -16t Check your answer using the FOIL method. -16t Repeat, using the first term in the bottom row: t  2t = - 8

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8 Use the Remainder Theorem Remainder Theorem If the polynomial P(x) is divided by x – a, the remainder is equal to P(a).