Do Now 3/5/10

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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)
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HomeworkPunchline worksheet 13.5

• What Happened to the Guy Who
• Lost the Pie-Eating Contest

He came in sickened
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Objective

• SWBAT factor trinomials of the
  form ax² bx c

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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)
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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)
3x 1 0 x 1/3
x 5 0 x -5
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Factoring When a is Negative
-4x² 12x 7
First factor -1 from each term in the trinomial
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
(2x 1)(2x 7)
(2x 1)(2x 7)
Dont forget about the negative you factored from
the beginning!!
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A shortcutfor 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

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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 )
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Factoring polynomialsTry 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)
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Try it outFactoring When a is NegativeSolve
the Equation
-2x² 5x 3
First factor -1 from each term in the trinomial
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)
(x 3)(2x 1)
Dont forget about the negative you factored from
the beginning!!
2x 1 0 x -1/2
x - 3 0 x 3
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Problem Solving

• A rectangles 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
Cant have negative width
Dimensions 15 x 2/3
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Homework
How Do You Park a Computer??Punchline activity

• Text p. 596, 4 44 multiples of 4