1. Multiplying Polynomials January 29, 2009

2. Page 416-417 #10-38 even 10) terms: 5x 3, x; coefficients: 5, 1 12) term: 7x 2 ; coeff: 7 14) monomial 16) monomial 18) Not a polynomial 20) Not classified (quadnomial) 22) binomial 24) 3x 3 + 5x 2 +4, degree is 3 26) x 2 –x+4, degree is 2 28) x 17 -3x 4, degree is 17 30) 15, 0 32) 5, -15 34) 34, 34 36) -1, 19 38) 0, 0

3. Objectives Find the product of a monomial and a polynomial. Find the product of two polynomials. Square a polynomial. Find the product of two binomials that differ on in sign.

4. Multiplying a polynomial by a monomial Use the distributive property to multiply each term in the polynomial by the monomial. x(2x+1) 2x 2 +2x

5. Multiplying polynomials Method 1: The Distributive Property 1.Distribute the first binomial over the second binomial. 2.Multiply. 3.Combine like terms. (2x+1)(x-5) = 2x(x-5)+1(x-5) = 2x 2 -10x+x-5 = 2x 2 -9x+5

6. Multiplying polynomials Method 2: FOIL (only works for binomials) 1.Multiply the FIRST term of each binomial. 2.Multiply the OUTER term of each binomial. 3.Multiply the INNER term of each binomial. 4.Multiply the LAST term of each binomial. 5.Combine like terms. (3x-1)(2x+2) F O I L 6x 2 +6x -2x -2 = 6x 2 +4x-2

7. Multiplying Polynomials Method 3: Completing the square. 1.Write each binomial along the sides of a square… 2.Multiply each item… 3.Add the items together… 4.Combine like terms. (3x+4)(2x+1) 6x 2 +8x+3x+4 6x 2 +11x+4 6x 2 8x 3x4

9. Multiplying polynomials Method 4: Vertical Method 1.Line up the polynomials. 2.Multiply each term, like compound multiplication. 3.Add. 4.Combine like terms. x 2 +3x +5 x -2. -2x 2 -6x -10 x 3 +3x 2 +5x. x 3 +x 2 -x -10

10. Squaring a polynomial While you can use the methods for multiplying polynomials, there is a shortcut! 1.Square the first term. 2.Multiply the product of the two terms by two. 3.Square the last term. For example: (x+5) 2 x 2 +(x*5*2)+25 x 2 +10x+25

11. The product of two binomials that differ only in sign Again, you can use the methods of multiplying polynomials… but why waste time! 1.Square the first term 2.Subtract the square of the second term from the answer in 1. Example: (3x-9)(3x+9) 9x 2 -81

12. 4.5, pages 441-443 #2-76 even