Factor completely 10x2 + 2x − 8

First, notice every term has a common factor of 2, so factor out a 2.

[tex] 10x^2 + 2x - 8 = [/tex]

[tex] = 2(5x^2 + x - 4) [/tex]

Now we need two numbers that multiply to 5 and two numbers that multiply to -4.
For the 5, it is a single possibility, 5 and 1, so we will have

[tex] = 2(5x~~~~~~)(x~~~~~~) [/tex]

Pairs of numbers that multiply to -4 are:
-4, 1
4, -1
2, -2

We need to choose the correct pair and place it in the correct order.
To do that, we place the numbers as guesses and multiply out the factors to see if we get the correct middle term.

First guess: -4, 1

[tex] = 2(5x - 4)(x + 1) [/tex]

The middle term would be: 5x - 4x = x, which is what we want, so we lucked out and we have the answer with just one guess.

Answer: [tex]10x^2 + 2x - 8 = 2(5x - 4)(x + 1) [/tex]