Answer to Question #12427 in Algebra for christen

Question

How do you factor 6x^2+15x-36?

Answer 1

To factor 6x^2+15x-36 we need to find roots of the equation 6x^2+15x-36=0.
x1,2=(-15+-sqrt(225+36*24))/12=(-15+-33)/12. Therefore x1=(-15+33)/12=18/12=3/2, x2=(-15-33)/12=-4
So due to factor theorem we obtain
6x^2+15x-36=6(x-(-4))(x-3/2)=6(x+4)(x-3/2)=3(x+4)(2x-3)