 Carol Gates

2021-09-07

Factor using the method indicated
a) Use GCF: $9x{y}^{2}+6xy$
b) Use sum and product: ${x}^{2}-3x-40$
c) Use GCF, then Sum and product $4{x}^{2}-68x+240$ Mayme

Expert

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

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