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Math 9 Factoring using Decomposition

Math 9 Factoring using Decomposition. Learning Outcome – to be able to factor using decomposition. Factoring using Decomposition. Example: Factor , where a,b , and c are numbers.

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Math 9 Factoring using Decomposition

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  1. Math 9 Factoring using Decomposition Learning Outcome – to be able to factor using decomposition

  2. Factoring using Decomposition Example: Factor , where a,b, and c are numbers Step 1: Need to find two numbers that multiply together to give you ( )( )=ac (or just c if a=1) and those same two numbers need to add together to give you ___+___=b Step 2: Rewrite the expression replacing the middle term with new numbers Step 3: Now you have 4 terms in the polynomial, group them into pairs Step 4: Factor each set of brackets using GCF method Step 5:Record answer; looks like (GCFs)(common leftovers)

  3. Factoring using Decomposition Example: Factor Step 1: Need to find two numbers that multiply together to give you ( )( )=-8 and those same two numbers need to add together to give you ___+___=-2 -4 2 -4 2 Step 2: Rewrite the expression replacing the middle term with new numbers Step 3: Now you have 4 terms in the polynomial, group them into pairs Step 4: Factor each set of brackets using GCF method x(x-4) Step 5:Record answer; looks like (GCFs)(common leftovers) (x

  4. Factoring using Decomposition Example: Factor Step 1: ( )( )=2 ___+___=3 1 2 1 2 Step 2: These are ALWAYS the same or else you did something wrong! Step 3: x(x+1) Step 4: Step 5:Record answer; looks like (GCFs)(common leftovers) (x Step 5: Check by multiplying – USE FOIL

  5. Factoring using Decomposition Check by Expand and Simplify: (x+2)(x+1) (2)(1) (2)(x)+ =(x)(x)+ (x)(1)+ = = If it is the same as the original question then you have it right

  6. Factoring using Decomposition Example: Factor Step 1: ( )( )=-14 ___+___=5 -2 7 -2 7 Step 2: These are ALWAYS the same or else you did something wrong! Step 3: x(x-2) Step 4: Step 5:Record answer; looks like (GCFs)(common leftovers) (x Step 5: Check by multiplying – USE FOIL

  7. Factoring using Decomposition Check by Expand and Simplify: (x+7)(x-2) (7)(-2) (7)(x)+ =(x)(x)+ (x)(-2)+ = = If it is the same as the original question then you have it right

  8. Factoring using Decomposition Example: Factor Step 1: ( )( )=-16 ___+___=-6 2 -8 2 -8 Step 2: These are ALWAYS the same or else you did something wrong! Step 3: x(x+2) Step 4: Step 5:Record answer; looks like (GCFs)(common leftovers) (x Step 5: Check by multiplying – USE FOIL

  9. Factoring using Decomposition Check by Expand and Simplify: (x-8)(x+2) (-8)(2) (-8)(x)+ =(x)(x)+ (x)(2)+ = = If it is the same as the original question then you have it right Do you see a pattern for the two numbers that you found to multiply together and add together and the final answer? ONLY WORKS FOR A SIMPLE TRINOMIAL , where a = 1

  10. Assignment Factoring using Decomposition Due Thursday, December 20th Quiz Friday, December 21st

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