Question

(Different one) Factor 6x^2 - 10x - 4

Answer 1

We can first factor all the terms by 2:
6x^2 - 10x - 4=2(3x^2-5x-2)

Then we solve 3x^2-5x-2=0.

Discriminant : 25+4*3*2=49=7^2 hence the roots are (5-7)/6 and (5+7)/6 which are -1/3 and 2

Hence 3x^2-5x-2=(x-2)(3x+1)

Thus 6x^2-10x-4=2(x-2)(3x+1)

Answer 2

$6 x^{2} -10x-4$ =

= $6 x^{2} -12x+2x-4$ =

= 6x(x-2)+2(x-2) =

= (x-2)(6x+2) =

= 2(x-2)(3x+1)


or

Let's solve the equation:

$6 x^{2} -10x-4$ = 0

Discriminant:

Δ = $10^{2} -4*6*(-4)$ = 196 = $14^{2}$

The roots are:

x1 = $\frac{10+14}{2*6}$ = $\frac{24}{12}$ = 2

x2 = $\frac{10-14}{2*6}$ = $\frac{-4}{12}$ = $\frac{-1}{3}$

so:

$6 x^{2} -10x-4$ = 6(x-2)(x+$\frac{1}{3}$) = (x-2)(6x+2) = 2(x-2)(3x+1)