Conqueror
Answered

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(Different one)

Factor 6x^2 - 10x - 4

Sagot :

Hippalectryon
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)
mariangel
[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)
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