Do Now 3/5/10 Take out HW from last night.

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Do Now 3/3/10  Take out HW from last night. Text p. 578, #4-48 multiples of 4  Copy HW in your planner. Text p. 586, #4-52 multiples of 4  In your notebook,

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Do Now 3/5/10 Take out HW from last night. Punchline worksheet 13.5 Copy HW in your planner. Text p. 596, #4 – 44 multiples of 4 Try to factor the following polynomial of the form ax² +bx + c. 6y² – 5y – 4 (3y – 4)(2y + 1)

Homework Punchline worksheet 13.5 “What Happened to the Guy Who Lost the Pie-Eating Contest” He came in sickened

Objective SWBAT factor trinomials of the form ax² + bx + c

Section 9.6 “Factor ax² + bx + c” 2x² – 7x + 3 First look at the signs of b and c. Factors of 2 Factors of 3 Possible factorization Middle term when multiplied 1, 2 1, 3 (x – 1)(2x – 3) -3x – 2x = -5x 3, 1 (x – 3)(2x – 1) -x – 6x = -7x (x – 3)(2x – 1)

Factor ax² + bx + c. Solve the equation. 3x² + 14x - 5 First look at the signs of b and c. Factors of 3 Factors of -5 Possible factorization Middle term when multiplied 1, 3 1, -5 (x + 1)(3x – 5) -5x + 3x = -2x 1,3 -1, 5 (x – 1)(3x + 5) 5x – 3x = 2x 5, -1 (x + 5)(3x – 1) -x + 15x = 14x -5, 1 (x – 5)(3x + 1) x – 14x = -13x (x +5)(3x – 1) x + 5 = 0 x = -5 3x – 1 = 0 x = 1/3

Factoring When ‘a’ is Negative First factor -1 from each term in the trinomial -4x² +12x + 7 Now look at the signs of b and c. – (4x² – 12x – 7) Factors of 4 Factors of -7 Possible factorization Middle term when multiplied 1, 4 1, -7 (x + 1)(4x – 7) -7x + 4x = -3x -1, 7 (x – 1)(4x + 7) 7x – 4x = 3x 7, -1 (x + 7)(4x – 1) -x + 28x = 27x -7, 1 (x – 7)(4x +1) x - 28x = -27x 2, 2 (2x + 1)(2x – 7) -14x +2x = -12x (2x – 1)(2x + 7) 14x – 2x = 12x Don’t forget about the negative you factored from the beginning!! – (2x + 1)(2x – 7) (2x + 1)(2x – 7)

A shortcut… for factoring ax² + bx + c (1) multiply ‘a’ and ‘c’ together to get new ‘c’ term. Write new polynomial (keep ‘b’ term the same and make ‘a’ = 1) (2) factor new polynomial normally. (3) divide number terms of binomial by ‘a’. (4) simplify fractions. (5) move denominator of fractions in front of variable terms of binomials

Factor ax² + bx + c, using a shortcut… 8x² – 14x – 15 (1) multiply ‘a’ and ‘c’ together to get new ‘c’ term. Write new polynomial (keep ‘b’ term and make ‘a’ = 1) (2) factor new polynomial normally. (3) divide number terms of binomial by ‘a’. (4) simplify fractions. (5) move denominator of fractions in front of variable terms of binomials (x – 20 )(x + 6 ) 8 8 (x – 5 )(x + 3 ) 2 4 2 4 ( x – 5)( x + 3 )

Factoring polynomials…Try it out… First look at the signs of b and c. 3t² + 8t + 4 4t² - 9t + 5 (t + 2)(3t + 2) (t – 1)(4t – 5)

Try it out…Factoring When ‘a’ is Negative…Solve the Equation First factor -1 from each term in the trinomial -2x² +5x + 3 Now look at the signs of b and c. – (2x² – 5x – 3) Factors of 2 Factors of 3 Possible factorization Middle term when multiplied 1, 2 1, -3 (x + 1)(2x – 3) -3x + 2x = -x -1, 3 (x – 1)(2x + 3) 3x – 2x = x 3, -1 (x + 3)(2x – 1) -x + 6x = 5x -3, 1 (x – 3)(2x +1) x - 6x = -5x Don’t forget about the negative you factored from the beginning!! – (x – 3)(2x + 1) (x – 3)(2x + 1) x - 3 = 0 x = 3 2x + 1 = 0 x = -1/2

Problem Solving w 3w + 13 w = -5 w = 2/3 Can’t have negative width A rectangle’s length is 13 meters more than 3 times its width. The area is 10 square meters. What are the dimensions of the rectangle? Area = length x width w 3w + 13 Substitute the solution to see the dimensions of the rectangle. (2/3) w = -5 w = 2/3 3(2/3)+13 Can’t have negative width Dimensions: 15’ x 2/3’

How Do You Park a Computer?? Punchline activity Homework Text p. 596, #4 – 44 multiples of 4