SOLUTION: Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now th

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now th      Log On


   

Question 969380: Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now the equation looks like this:
15x^2 + 6x - 30x - 12. So I divide: 15x^2 + 6x/2x and -30x-12/-6 which now gave me 3x(5x+2)-6(5x+2) I continue to think my answer is (5x+2)(3x-6). unfortunately, the answer key has the answer as 3(5x+2)(x-2) what did I do wrong? Please help me.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Each term has a factor of 3:
15x%5E2+-+24x+-+12
3%285x%5E2-8x-4%29

There are only so few ways to factorize -4. Try a few combination of trinomial factorizations for the quadratic factor from the last step.

Look at the possible result for terms of x:

(5 2)(1 2)----------10 and 2, maybe.

(5 4)(1 1)---------5 and 4, NO.

(5 4 )(1 1)----------5 and 4, NO.

Look further at this: %285x+%2B-+2%29%28x%2B-+2%29;
You need -8x and -4. Decide which signs within the binomials are needed.
......
This is what works: %285x%2B2%29%28x-2%29.

Your originally given expression also contained a factor of 3, so to finish your factorization of that, you have
highlight%28highlight%283%285x%2B2%29%28x-2%29%29%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Hello. I am trying to factor this equation 15x^2 - 24x - 12. I then multiplied 15 x -12 = -180. From here I need to found -30 x 6 which if you subtract 6 from -30 = -24. so now the equation looks like this:
15x^2 + 6x - 30x - 12. So I divide: 15x^2 + 6x/2x and -30x-12/-6 which now gave me 3x(5x+2)-6(5x+2) I continue to think my answer is (5x+2)(3x-6). unfortunately, the answer key has the answer as 3(5x+2)(x-2) what did I do wrong? Please help me.
First, this is NOT an equation, but a TRINOMIAL that can be FACTORED.

15x%5E2+-+24x+-+12

The first step you need to take is to find the GCF

3%285x%5E2+-+8x+-+4%29 ------ Factoring out GCF, 3

highlight_green%283%285x+%2B+2%29%28x+-+2%29%29%29 ----- Factoring trinomial in the parentheses



Your answer is PARTIALLY correct. Since you didn't factor out a GCF, you can see that one of your

binomials, (3x - 6) can be factored as: 3(x - 2), thereby giving you: 3(x - 2)(5x + 2), which is

the same as mine and the answer in the answer key.