# Step i find the gcf of the coefficients gcf8 6 2 step

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Step I: Find the GCF of the coefficients. GCF(8, 6) = 2. Step II: Find the GCF of the variable parts. GCF( x 3 , x 2 ) = x 2 . Step III: Divide all the monomials by the GCFs and rewrite with the GCFs out front: 8 x 3 + 6 x 2 = + 2 2 2 3 2 2 6 2 8 2 x x x x x = 2 x 2 (4 x + 3) 3. Factor 18 y 3 ( x – 1) + 21 y ( x – 1) Step I: Find the GCF of the coefficients: GCF(18, 21) = 3. Step II: Find the GCF of the variable parts: GCF( y 3 ( x – 1), y ( x – 1)) = y ( x – 1) Step III: Divide all the monomials by the GCFs and rewrite with the GCFs out front: 18 y 3 ( x – 1) + 21 y ( x – 1) = - - + - - - ) 1 ( 3 ) 1 ( 21 ) 1 ( 3 ) 1 ( 18 ) 1 ( 3 3 x y x y x y x y x y = 3 y ( x – 1)(6 y 2 + 7) 6. Factor 3 ab + 7 b .

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Math 1300 Section 4.1 Notes 4 7. Factor -28 a 3 b 7 – 36 a 2 b 5 . 8. Factor 8 a 2 bc – 12 ab 2 c . 9. Factor 9 xy 3 + 27 xy x 5 . (Hint: What is the leading coefficient?) 10. Factor (9 – 3 x )(27 y 2 ) – (9 – 3 x )(15 y 3 )
Math 1300 Section 4.1 Notes 5 Factoring by Grouping If a polynomial contains four or more terms, it may be helpful to put the terms into groups of two and factor out a common factor from each of these groups. This is called grouping . Examples: 1. Factor x 2 y + 6 x + 3 xy 2 + 18 y Step I: Group the terms so that each group shares a common factor: x 2 y + 6 x + 3 xy 2 + 18 y = ( x 2 y + 6 x ) + (3 xy 2 + 18 y ) Step II: Factor out the common terms from each group: ( x 2 y + 6 x ) = x ( xy + 6) (3 xy 2 + 18 y ) = 3 y ( xy + 6) Step III: Rewrite the polynomial as the sum of the factored groups: x 2 y + 6 x + 3 xy 2 + 18 y = x ( xy + 6) + 3 y ( xy + 6) Step IV: Factor the resulting polynomial from Step III: x ( xy + 6) + 3 y ( xy + 6) = ( xy + 6)( x + 3 y ) 2. Factor 2 x 3 + 3 x 2 + 2 x + 3 Step I: Group the terms so that each group shares a common factor: 2 x 3 + 3 x 2 + 2 x + 3 = (2 x 3 + 3 x 2 ) + (2 x + 3) Step II:

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