1. 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)

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

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

4. 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)

5. 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

6. 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)

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

8. 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 )
(x – 5 )(x + 3 )
( x – 5)( x + 3 )

9. 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)

10. 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

11. 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’

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