Question

(Different one)

Factor 6x^2 - 10x - 4

Answer 1

`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 =
`(10+14)/(2*6)` =
`(24)/(12)` = 2

x2 =
`(10-14)/(2*6)` =
`(-4)/(12)` =
`(-1)/(3)`

so:


`6 x^(2) -10x-4` = 6(x-2)(x+
`(1)/(3)`) = (x-2)(6x+2) = 2(x-2)(3x+1)

Answer 2

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)