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5.4 F ACTORING P OLYNOMIALS Algebra II w/ trig

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1. GCF: Greatest Common Factor - it may be a constant, a variable, of a combination of both (3, X, 4X) Ex: x 2 + 7x = 2x 2 - 8x = 3x 2 - 6x + 3 =

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2. DOS: Check for a Difference of Squares - Are there only two terms? -Is the first term a perfect square? - Is the second term a perfect square? - Is there a minus between the two terms? If so: factor as (root of 1st + root of 2nd)(root 1 – root 2) Ex: 4x 2 - 361 =

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3. PTS: Perfect Trinomial Square - Is the first a perfect square? - Is the last a perfect square? - is the middle 2 ● root 1 st ● root last? If so, it factors as (root of 1st ± root of last)2 Use the middle sign Ex: x 2 -10x + 25 x 2 + 20x + 64

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4) AC Method: ax 2 + bx + c - Multiply a and c - Find factors of ac that add to equal b - Separate into two parentheses using the variable and the factors - If a is greater than 1, put it under each factor - Reduce the fractions if possible - If there is a number left in the denominator move it in front of the variable Ex: x 2 - 6x - 16

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When : Ex: 2x 2 - 5x – 12

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5. Grouping Used when there are 4 or more terms. Ex: 2ab + 14a + b + 7 (2ab +14a) + (b + 7) 2a(b+7) + 1(b+7) (b+7)(2a+1) Write what they have in common, and then write what’s left. Ex: xy + 3x – y 2 - 3y

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6) Sum/Difference of 2 cubes a 3 + b 3 = (a + b)(a 2 - ab + b 2 ) Ex: 64x 3 + 27 = a 3 – b 3 = (a-b)(a 2 + ab + b 2 ) Ex: 8x 3 -125 =

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7. How do I know what method to use? a. Binomial (2 terms) 1. GCF 2. Difference of Squares 3. Difference or Sum of Cubes b. Trinomials (3 terms) 1. GCF 2. Perfect Square Trinomial 3. AC Method c. Polynomials (4 or more terms) 1. GCF 2. Grouping If none of the above methods work then the polynomial is Prime (non factorable).

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Factor: 1.2. 3.4.

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5.6. 7.8.

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9.10. 11.12. 8r 3 – 64s 3 3ay + 6by + a + 2b 3x 3 +24

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