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Copy of Graphic Organizer for Factoring Polynomials

Math: Block 3
by

cathelyne joseph

on 17 February 2013

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Transcript of Copy of Graphic Organizer for Factoring Polynomials

Greatest Common Factor Prime Polynomials Difference of Squares Trinomials with a=1 Trinomials with a not equal to 1 Perfect Square Trinomials Factoring Polynomials 18x +6x - 12x 2 3 Step 1: Find the GCF 18x 6x 2 3 -12x 1, 2, 3, 6, 9, 18 ,x ,x , x 1, 2, 3, 6, x, x 1, 2, 3, 4, 6,12, x The GCF is 6x Step 2: Factor out the GCF 18x /6x = 3x 3 2 -12x/6x = -2x 6x/6x = x 2 2 Solution: 6x(3x + x - 2) a - 16 2 Both terms are perfec squares The formula is a - b = (a+b)(a-b) 2 2 a - 4 2 2 (a + 4)(a - 4) Final Solution: replace 16 with 4 2 4 = b 2 25x - 30x + 9 2 Rule: a x +2abx + b = (ax +b) 2 2 2 2 25 = a b = 9 2 2 a =(+,-)5 b =(+,-)3 2ab = -30 We know that (a)(b) must = -15
So we make 1 positive and 1 negative Final Solution: (5x -3) 2 x + 8x + 15 2 Step 1: Find the factors of 15 15x: 1, 3, 5, 15 Which two add up to 8 Step 2: Insert into the top right and bottom left corners of the box (when using box method)
x 2 +15 3x 5x Step 3: Find the GCF of the rows and columns 5 x x 3 + + Step 4: Write in standard form (this is your final solution) (x+3)(x+5) or If you know that with this form of trinomials the answer is always in (x+a)(x+b) format then you can skip steps 2-4 and write the factors into the solution format. a b 2x +14x + 3 2 This polynomial is prime which means that its only factors are 1 and itself. This means that it cannot be simpliflied 4x + 4x - 15 2 Step 1: multiply a and c a b c (4)(-15) = -60 Step 2: Find the factors of ac with a sum equal to b -60x: +,-(1, 2, 3, 4, 5, 6, 10, 12, 15, 30, 60) Step 3: Insert the factors into the top right and bottom left areas of the box. 4x 2 -15 10x -6x Step 4: Find the GCF of the rows and columns 2x 5 - + 3 2x Step 5: Write in standard form (2x-3)(2x+5) Polynomials with 4 terms x +2x +18x + 36 3 4 Step 1: Divide the polynomials into two groups (x + 2x )(18x+36) 3 4 Step 2: Find the GCF of each group x (x+2) + 18(x+2) 3 Step 4: Combine the x and the 18 and multiply that by (x+2) (x + 18)(x + 2) 3 Final Answer By Waverly Gesrich- Thompson
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