Objectives: Students will be able to.. Add, subtract and multiply polynomials.

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Objectives: Students will be able to.. Add, subtract and multiply polynomials

 Add or subtract coefficients of like terms  Can add or subtract vertically or horizontally EXAMPLE: Add the polynomials (5x 2 +x-7)+(6x-3x 2 -1) Vertically:Horizontally: (5x 2 +x-7)+(6x-3x 2 -1)

Vertically: (3x 3 +8x 2 -x-5) -(5x 3 -x 2 +17) Horizontally: (3x 3 +8x 2 -x-5)-(5x 3 -x 2 +17)

Vertically: 4x 2 + x -5 2x +1 Horizontally: (4x 2 + x- 5)(2x + 1)

1.(x+2)(5x 2 +3x -1)2. (x-2)(x-1)(x+3)

(x+5) (x+7)(-x+1)

Sum and DifferenceExample: (a +b) (a –b) = a 2 – b 2 (2x+1)(2x-1)= (2x) 2 –(1) 2 =4x 2 -1 Square of a BinomialExamples: (a + b) 2 = a 2 +2ab +b 2 (x + 3) 2 = x 2 + 2(x)(3) = x 2 +6x+9 (a – b) 2 = a 2 – 2ab + b 2 (x - 3) 2 = x 2 - 2(x)(3) = x 2 -6x+9

Cube of a PolynomialExamples: (a + b) 3 = a 3 + 3a 2 b+3ab 2 + b 3 (x+2) 3 = (x) 3 +3(x) 2 (2)+3(x)(2) 2 +(2) 3 = x 3 + 6x x +8 (a - b) 3 = a 3 - 3a 2 b+3ab 2 - b 3 (x-2) 3 = (x) 3 -3(x) 2 (2)+3(x)(2) 2 -(2) 3 = x 3 - 6x x -8

 Helps to know coefficients when expanding binomials

1. (3x – 2)(3x + 2) 2. (5a + 2) 2 3. (2m – 3) 3

1.) (4x – 5)(4x +5 ) 2.) (6-x 2 ) 2 3.)(3x+7) 3

From 2000 through 2009, the amount spent per week for food by a typical employee of a company is T = x 3 – 0.561x x + 50, where x is the number of years since The amount per employee spent for food prepared at home is H = 0.185x x +25. The number of employees is E = 2.5x Write a model for the total amount N that employees spent per week for food not prepared at home.