3.4 Day 2 Factoring Polynomial Expressions.notebook
3-4 Day 2 Factoring Polynomial
Expressions
November 12, 2015
Steps for factoring:
1. Factor out GCF
2. What's left?
I can...
Factor polynomial expressions
- Quadratic or Quartic? Factor normally
- Are there 4 terms? Factor by grouping
- Is it a sum or difference of perfect cubes?
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Factor by Grouping: 4 terms
x3 – 2x2 – 9x + 18
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Example 1:
a) 8r3 - 64r2 + r - 8
Step 1: Group the first two terms and the second two terms together
with a plus sign between them.
(x3 – 2x2) + (– 9x + 18)
Step 2: Factor out the GCF from each group.
x2(x – 2) + -9(x - 2)
b) 12x3 + 2x2 - 30x - 5
Notice, these are the same
Step 3: Re group. Put GCF's in one group, and the "left-overs" in a
second group.
(x2 - 9)(x - 2)
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Sum of Cubes: adding 2 terms that are
perfect cubes (ex: 8, 27, 64, 125, x3, 8x3, ...)
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How to use this formula:
a3 + b3 = (a + b)(a2 – ab + b2)
x3 + 8
You will use this formula to factor:
Step 1: Break down both terms:
a3 + b3 = (a + b)(a2 – ab + b2)
(x)3 + (2)3
Step 2: Label the first term a and the second term b:
(x)3 + (2)3
a
Step 3: Plug into formula:
b
(a + b)(a – ab + b2)
2
(x + 2)((x)2 – (x)(2) + (2)2)
Step 4: Simplify:
(x + 2)(x2 – 2x + 4)
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3.4 Day 2 Factoring Polynomial Expressions.notebook
Example 2: Factor completely
27a3 + 125
November 12, 2015
Difference of Cubes: subtracting 2 terms
that are perfect cubes (ex: 8, 27, 64, 125, x3,
8x3, ...)
You will use this formula to factor:
a3 - b3 = (a - b)(a2 + ab + b2)
Almost exactly the same as the SUM of cubes, just different signs
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Example 3: Factor Completely
a3 - b3 = (a - b)(a2 + ab + b2)
8x3 – 1
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Example 4: Factor Completely
a) 5x3 – 40
b) 2x3 + 128
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DON'T FORGET:
1. Factor out GCF
2. What's left?
- Quadratic or Quartic? Factor normally
- Are there 4 terms? Factor by grouping
- Is it a sum or difference of perfect cubes?
Jun 16-7:53 AM
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