Polynomials and Polynomial Functions *Chapter 5 Polynomials and Polynomial Functions

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

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

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.

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

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

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.

Example 4 : Answer

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.

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

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 + 5. 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.