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)