Question

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

so far I factored out 2: 2(x^2 + 9x - 5)
what's the next step?

Answer 1

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).