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

Chapter 6 - Section 6.2 - Exercise Set: 49 (Answer) $4x^2y + 4xy - 12y$ = $4y(x^2 + x - 3)$
Chapter 6 - Section 6.2 - Exercise Set: 49 (Solution) Factorize : $4x^2y + 4xy - 12y$ First step : Take out the GCF of $4x^2y$, $4xy$ and $12y$ which is $4y$ $4x^2y + 4xy – 12y$ = $4y(x^2 + x - 3)$ Take $(x^2 + x - 3)$ to be $(x + \triangle)(x + \square)$ For this, we have to look for two numbers whose product is -3 and whose sum is +1. Factors of -3 $\Longleftrightarrow$ Sum of Factors 1,-3 $\Longleftrightarrow$ -2 (Incorrect sum) -1,3 $\Longleftrightarrow$ 2 (Incorrect sum) As there are no two numbers that can have a product of -3 and a sum of +1, no further factorization can be done with $(x^2 + x - 3)$. Thus, $4x^2y + 4xy - 12y$ = $4y(x^2 + x - 3)$