[tex]6 x^{2} -10x-4[/tex] =
= [tex]6 x^{2} -12x+2x-4[/tex] =
= 6x(x-2)+2(x-2) =
= (x-2)(6x+2) =
= 2(x-2)(3x+1)
or
Let's solve the equation:
[tex]6 x^{2} -10x-4[/tex] = 0
Discriminant:
Δ = [tex] 10^{2} -4*6*(-4)[/tex] = 196 = [tex] 14^{2} [/tex]
The roots are:
x1 = [tex] \frac{10+14}{2*6} [/tex] = [tex] \frac{24}{12} [/tex] = 2
x2 = [tex] \frac{10-14}{2*6} [/tex] = [tex] \frac{-4}{12} [/tex] = [tex] \frac{-1}{3} [/tex]
so:
[tex]6 x^{2} -10x-4[/tex] = 6(x-2)(x+[tex] \frac{1}{3} [/tex]) = (x-2)(6x+2) = 2(x-2)(3x+1)
