A2 – Factoring Review 2
Factoring Patterns
Difference of Perfect Squares
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|Step 1: Factor out the GCF if there is one |[pic] |
|Step 2: Check whether you have difference of squares | |
|Step 3: Use difference of squares pattern to factor | |
|[pic] | |
|Practice: |
|[pic] [pic] [pic] |
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|[pic] [pic] [pic] |
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Sum and Difference of Cubes
|Perfect cubes: numbers whose factors can be written as a number times itself times itself like |
|64 = _______ |
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|Sum or Difference of Cubes: Use for two terms that are perfect cubes with a ________ or __________ sign between the terms. |
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|Sum of cubes: a3 + b3 = | x3 + 27 = |
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|_________________________ | |
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|Difference of cubes: a3 – b3 = | 64a3 – 27= |
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|_________________________ | |
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|( Always look for a ______________________________, ______ first! |
|( Check the ______________________ next to see if you can factor any further. |
|PRACTICE: Factor the following polynomials. |
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|-54x3 + 150 10x4 – 80x |
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|2x4 + 3x3 + 2x + 3 |
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Perfect Square Trinomials
|Perfect square trinomials have the following pattern: | |
| |1x2 + 2x + 1 |
|a2 + 2ab + b2 = (a + b)(a + b) = _____________ | |
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|a2 - 2ab + b2 = (a - b)(a - b) = _____________ |4x2 – 12x + 9 |
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|You can factor them by grouping, but knowing the pattern makes the factoring easier. |
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|**Remember to take out the _____________________________ first! |
|a) x2 - 8x + 16 |b) 9y2 + 60y + 100 |
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|a)________________________ |b)_________________________ |
|c) 2y4 + 20y2 + 50 |d) 2x2 - 12xy + 18y2 |
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|c)________________________ |d)_________________________ |
Additional Practice: Factor completely
| x5- x3 + 8x2- 8 |
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