A company surveyed both adults and children about whether or not they liked a particular
game. The survey results are shown in the table.

Here are the steps:

We start with 10x^2 - 23x - 5

We need to find factors of ac (in this case, 10 and -5 or -50) that add to equal -23.

These are -25 and +2

Rewrite the problem by separating the middle term into two:

10x^2 + 2x - 25x - 5

From the first two terms, factor out the GCF (2x).

From the next two terms, factor out the GCF (-5).

Your first binomial is therefore (2x - 5).

Now divide ether 2x from the first two terms or -5 from the last two terms. Both will get you the same result: (5x + 1). That is your second binomial.

(2x - 5)(5x + 1) is your final answer.