## Algebra: A Combined Approach (4th Edition)

Chapter 6 - Section 6.2 - Exercise Set: 69 (Answer) $x^3y^2 + x^2y - 20x$ = $x(xy + 5)(xy - 4)$
Chapter 6 - Section 6.2 - Exercise Set: 69 (Solution) Factorize : $x^3y^2 + x^2y - 20x$ First step : Take out the GCF of $x^3y^2$, $x^2y$ and $20x$ which is $x$. $x^3y^2 + x^2y - 20x$ = $x(x^2y^2 + xy - 20)$ Take $(x^2y^2 + xy - 20)$ to be $(xy + \triangle)(xy + \square)$ For this, we have to look for two numbers whose product is -20 and whose sum is 1. Factors of -20 $\Longleftrightarrow$ Sum of Factors 1,-20 $\Longleftrightarrow$ -19 (Incorrect sum) 2,-10 $\Longleftrightarrow$ -8 (Incorrect sum) 4,-5 $\Longleftrightarrow$ -1 (Incorrect sum) 5,-4 $\Longleftrightarrow$ 1 (Correct sum, so the two numbers are 5 and -4) 10,-2 $\Longleftrightarrow$ 8 (Incorrect sum) 20,-1 $\Longleftrightarrow$ 19 (Incorrect sum) Thus, $x^3y^2 + x^2y - 20x$ = $x(xy + 5)(xy - 4)$