3.8Factoring.notebook 1 February 28, 2013

3.8Factoring.notebook
February 28, 2013
1
3.8Factoring.notebook
February 28, 2013
3.8 Factoring Quadratic Expressions
Recall expanding:
(2x - 3)(x + 4) = 2x2 + 5x - 12
Expanded form
Factored form
By expanding, we can go from factored form to standard form.
Factoring is the opposite of expanding. It "undoes" the
expansion.
We need to get from
to
2x2 + 5x - 12
(2x - 3)(x + 4)
By factoring, we can go from standard form to factored form.
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3.8Factoring.notebook
February 28, 2013
Factor the following:
x2 + 8x - 20
Think - we
need two
numbers
that...
add to 8
x (20)
1, 20
1, 20
4, 5
4, 5
10, 2
multiply to -20
Sum
19
19
1
1
Good, we found them!
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x2 + 8x - 20 = (x + 10)(x - 2)
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3.8Factoring.notebook
x2 - 2x - 15 =
Add to -2
Multiply to -15
x2 + x + 12 =
Add to 1
Multiply to -12
Uh oh, what does this mean?
February 28, 2013
x (-15)
Sum
-3, 5
2
3, -5
-2
x (+12)
Sum
1, 12
13
-1, -12
-13
3, 4
7
-3, -4
-7
2, 6
8
-2, -6
-8
x2 + x + 12 cannot be factored!
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3.8Factoring.notebook
February 28, 2013
Think graphically...
y = x2 - 2x - 15
is the same as
y = (x + 3)(x - 5)
Zeros at x = -3 and x = 5
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3.8Factoring.notebook
February 28, 2013
y = x2 + x + 12 has no equivalent in factored form. This is not a
problem, it just means that....
...the parabola has no zeros.
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3.8Factoring.notebook
3x2 - 6x - 45
February 28, 2013
= 3(x2 - 2x - 15)
Notice the common factor of 3
= 3(x + 3)(x - 5)
2x2 + 10x + 12
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3.8Factoring.notebook
3x2 - 11x - 4
February 28, 2013
Hmmm... no common factor
We need two numbers that multiply to 3 x (-4) = -12 and add to -11.
We get -12 and 1.
(-12)(1) = -12
(-12) + 1 = -11
3x2 - 11x - 4
= 3x2 + (1 - 12)x - 4
= 3x2 + x - 12x - 4
= x(3x + 1) - 4(3x + 1)
= (x - 4)(3x + 1)
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3.8Factoring.notebook
February 28, 2013
3x2 - 5x - 2
Homework: page 307 #
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