Factor the following: 4x^2 + 18x - 10

so far I factored out 2: 2 (x^2 + 9x - 5)

what's the next step?

Your input: factor 4x2+18x-10.

Factor the common term:

(4x2+18x-10) = (2 (2x2+9x-5))

To factor the quadratic function 2x2+9x-5, we should solve the corresponding quadratic equation 2x2+9x-5=0.

Indeed, if x1 and x2 are the roots of the quadratic equation ax2+bx+c=0, then ax2+bx+c=a (x-x1) (x-x2).

Solve the quadratic equation 2x2+9x-5=0.

The roots are x1=12, x2=-5 Therefore, 2x2+9x-5=2 (x-12) (x+5).

2 (2x2+9x-5) = 2 (2 (x-12) (x+5))

Simplify: 4 (x-12) (x+5) = 2 (x+5) (2x-1).

Thus, 4x2+18x-10=2 (x+5) (2x-1).

Answer: 4x2+18x-10=2 (x+5) (2x-1).