Factor using the method indicated a) Use GCF: 9xy2+6xy b) Use sum and product: x2−3x−40 c) Use GCF, then Sum and product 4x2−68x+240

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a) The given expression is, 9xy2+6xy The GCF of the two terms is 3xy. Hence, the required factorization is 3xy(3y+2). b) The given polynomial is, x2−3x−40 Let there be two numbers such that, a+b=−3 ab=−40 Then, a=−8,b=5. Thus, the given polynomial becomes, x2−8x+5x−40 ⇒x(x−8)+5(x−8) ⇒(x−8)(x+5) Thus, the required factorization is, (x−8)(x+5). The given polynomial is, 4x2−68x+240 The GCF of the terms is, 4. Hence, the required factorization using GCF method is 4(x2−17x+60) Consider the polynomial, (x2−17x+60) Let a and b be two numbers such that, a+b=−17 ab=60 Hence, a=−12,b=−5 Thus, the given polynomial becomes, x2−12x−5x+60 ⇒x(x−12)−5(x−12) ⇒(x−12)(x−5) Thus, the required factorization is, 4(x−12)(x−5)

Factor using the method indicated. a) Use GCF: 9xy^2+6xy. b) Use sum and product: x^2-3x-40

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