Factor using the method indicated a) Use GCF: 9xy2+6xy b) Use sum and product: x2−3x−40...

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