Do Now 3/5/10
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Take out HW from last night.
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Punchline worksheet 13.5
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Copy HW in your planner.
 Text p. 596, #4 – 44 multiples of 4
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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
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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
1, 2
3, 1
(x – 3)(2x – 1)
-x – 6x = -7x
(x – 3)(2x – 1)
2x
2
 x  6x  3
2x  7x  3
2
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
1,3
5, -1
(x + 5)(3x – 1)
-x + 15x = 14x
1, 3
-5, 1
(x – 5)(3x + 1)
x – 14x = -13x
(x +5)(3x – 1)
x+5=0
x = -5
3x – 1 = 0
x = 1/3
3x
2
 x  14x  5
3x  14 x  5
2
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, 4
-1, 7
(x – 1)(4x + 7)
7x – 4x = 3x
1, 4
7, -1
(x + 7)(4x – 1)
-x + 28x = 27x
1, 4
-7, 1
(x – 7)(4x +1)
x - 28x = -27x
2, 2
1, -7
(2x + 1)(2x – 7)
-14x +2x = -12x
2, 2
-1, 7
(2x – 1)(2x + 7)
14x – 2x = 12x
Don’t forget about the
negative you factored
from the beginning!!
– (2x + 1)(2x – 7)
A shortcut…
for factoring ax² + bx + c
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(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
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(1) multiply ‘a’ and ‘c’ together to
get new ‘c’ term. Write new
polynomial (keep ‘b’ term and
make ‘a’ = 1)  120
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(2) factor new polynomial
normally.
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(3) divide number terms of
binomial by ‘a’.
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(4) simplify fractions.
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(5) move denominator of
fractions in front of variable
terms of binomials
x  14 x  120
2
(x – 20 )(x + 6 )
8
8
(x – 5 )(x + 3 )
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)
3t  2t  6t  4
4t  5t  4t  5
3t  8t  4
4t  9t  5
2
2
2
2
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, 2
-1, 3
(x – 1)(2x + 3)
3x – 2x = x
1, 2
3, -1
(x + 3)(2x – 1)
-x + 6x = 5x
1, 2
-3, 1
(x – 3)(2x +1)
x - 6x = -5x
– (x – 3)(2x + 1)
Don’t forget about the
negative you factored
from the beginning!!
x-3=0
x=3
2x + 1 = 0
x = -1/2
Problem Solving
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
10  w(3w  13)
10  3w 2  13w
3w + 13
0  3w2  13w  10
Substitute the solution to see the
dimensions of the rectangle.
0  (3w  2)( w  5)
3w  2  0 and w  5  0
(2/3)
3(2/3)+13
w = 2/3
w = -5
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