Factor 5x^2a^2 - 19xa^2 - 4a^2. Show your work.

First, factor out the a^2 because every term has it: a² (5x²-19x-4)

Next, focus on what's inside the parenthesis.

the factors of 5 is 1 and 5

the factor of - 4 is 1 and - 4, 4 and - 1 or 2 and - 2, or - 2 and 2

what we need is a factor of 5 multiplying a factor of 4, the other factor of 5 multiplying the other factor of 4, the sum of the products makes - 19

line up the factors like this:

1 - 4

5 1

multiply diagonally: 5 * (-4) = - 20, 1*1=1

Note that - 20 and 1 make a sum of - 19, so this pair of factors works.

(x-4) (5x+1)

the final answer is a² (x-4) (5x+1)