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Factoring 0-3

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Two Ways to Factor Using GCF Using Grouping Using Grouping Through Sums and Factors

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Greatest Common Factor First thing to do is make a table Put the terms in question along the top Focus on the numbers first Focus on the variables next The outside column, multiplied together is the GCF The last line are the remainders

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Greatest Common Factor Example 75225 75225 5 75225 51545 75225 51545 5 75225 51545 539 75225 51545 539 3 75225 51545 539 313 Multiply these numbers to get the GCF These are your remainders that would go into the parentheses GCF: 5*5*3 = 75

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Greatest Common Factor Example 4x 4 y + 8x 3 y 4x 4 y8x 3 y 4x 4 y8x 3 y 4 4x 4 y8x 3 y 4x4yx4y2x 3 y 4x 4 y8x 3 y 4x4yx4y2x 3 y x3x3 4x 4 y8x 3 y 4x4yx4y2x 3 y x3x3 xy2y 4x 4 y8x 3 y 4x4yx4y2x 3 y x3x3 xy2y y 4x 4 y8x 3 y 4x4yx4y2x 3 y x3x3 xy2y yx2 GCF: 4x 3 yRemainder: (x+2) Put it together: 4x 3 y(x+2)

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Factoring Using Grouping When factoring by grouping, you will combine the GCFs in one set of the parentheses The other set of parentheses will be the remainders NOTE: The remainders should be identical. If not, then you are not done

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Factor Using Grouping Example 5x(x - 7)-2(x - 7) Combine the GCFs (5x – 2) Rewrite the Remainders (x – 7) Final Answer:(5x – 2)(x – 7)

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Factor Using Grouping Example Divide the polynomial in half

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Factor Using Grouping Factor the first two terms 15x 3 - 6x 2 3x 2 (5x – 2) Factor the second two terms -25x + 10 -5(5x – 2)

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Factor Using Grouping Combine the GCFs (-3x 2 – 5) Rewrite the Remainders (5x – 2) Final Answer:(-3x 2 – 5)(5x – 2)

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Using Grouping Through Sums and Factors In order to use this, you will need to rewrite the problem so that it has 4 terms so that you may factor by grouping. Follow the chart below a*cSign of c Answerb

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Using Grouping Through Sums and Factors Example x 2 + 17x + 72 a*cSign of c Answerb 72Sign of c Answerb 72+ Answerb 72+ Answer+17 72+ 9, 8+17

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Using Grouping Through Sums and Factors Rewrite the original equation with the new “b” factors x 2 + 17x + 72 x 2 + 9x + 8x + 72 Factor by grouping x(x + 9)8(x + 9) (x + 8)(x + 9)

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