Factoring a trinomial

[lordbodom]

I am working a problem to find the GCF of 3 trinomials. I am having trouble factoring one of them. The trinomial is:

[6x(3)-10x^(2)-4x]

I factored with 2x to get: [2x{3x^(2)-5x-2}]

Now I cant figure out how to factor {3x^(2)-5x-2}. From the other exercies i have practiced, you factor the -2 and see what factorings fit to equal 5. I cant figure out how this fits since for 2, the factors would be 2,1? The solution says (3x+1)(x-2) and doing the multiplication i see that it is correct, but i am not understanding how to get this?

 

[lookagain]

I am working a problem to find the GCF of 3 trinomials. I am having trouble factoring one of them. The trinomial is:

[6x(3)-10x^(2)-4x]

I factored with 2x to get: [2x{3x^(2)-5x-2}]

Now I cant figure out how to factor {3x^(2)-5x-2}. From the other exercies i have practiced, you factor the -2 and see what factorings fit to equal 5. I cant figure out how this fits since for 2, the factors would be 2,1? The solution says > > (3x+1)(x-1) < < and doing the multiplication i see that it is correct, but i am not understanding how to get this?

There's a typo. The factorization of \(\displaystyle \ 3x^2 - 5x - 2 \ \) is (3x + 1)(x - 2).

 

[lordbodom]

There's a typo. The factorization of \(\displaystyle \ 3x^2 - 5x - 2 \ \) is (3x + 1)(x - 2).

Thank you. Typo fixed.

 

[lordbodom]

Careful Lord: 6x^3 - 10x^2 - 4x

You got to: 3x^2 - 5x - 2, which is correct...

If difficult to factor, set equal to 0 : 3x^2 - 5x - 2 = 0
Now use the quadratic formula.

Sorry about the typo...using the quadratic formula I get x=-10 and x=-2. Not sure where to go from there?

 

[lordbodom]

HUH? How did you manage that?

3x^2 - 5x - 2 = 0

x = [-(-5) +- SQRT(5^2 - 4(3)(-2)] / (2(3))

x = [5 +- SQRT(25 + 24)] / 6

x = (5 +- 7) / 6

x = 12/6 or x = -2/6

x = 2 or x = -1/3

Do you FOLLOW that?

I do. Im sorry im a mess, I was reading the WRONG problem in my notepad, was doing a few and for some reason I used the formula on the wrong one.

 

[lordbodom]

So we have: x = 2 or x = -1/3

So the factoring is: (x - 2)(3x + 1)

Follow that MeLord?

Got it! thank you for the help!

 

[tutor]

the factors for the given expression was (2x)(x-2)(3x+1)

the given expression 6x³ -10x²-4x

take 2x as common then, 2x[3x²-5x-2]

factors for 3x²-5x-2
3*2=6 now find factors for 6, while adding are subtract we should get 5 value
3*2=6 no
6*1=6 yes hence 6-1=5

3x²-6x+1x-2
3x(x-2)+1(x-2)
(x-2)(3x+1)

therefore the factors are (2x)(x-2)(3x+1)

 

[lookagain]

the factors for the given expression was (2x)(x-2)(3x+1)

the given expression 6x³ -10x²-4x

take 2x as common then, 2x[3x²-5x-2]

factors for 3x²-5x-2
3*2=6 now find factors for 6, while adding are subtract we should get 5 value
3*2=6 no
6*1=6 yes hence 6-1=5

3x²-6x+1x-2
3x(x-2)+1(x-2)
(x-2)(3x+1)

> > > Therefore, the factors are 2x, x - 2, and 3x+1. < < <

The *factorization* is 2x(x-2)(3x+1).

 

[HallsofIvy]

It took me a moment to get it but LookAgain's point is that "the factors are" 2x, x- 2, and 3x+1. 2x(x- 2)(3x+ 1) is "the factorization" or "way of factoring", not just "the factors".