SOLUTION: Solve: 12x^3 + 12x^2 - 9x = 0 I forgot how to factor when the first term has an exponent of 3... Here is what I have so far which isn't much. 3x(3x^2 + 3)(4x - 3)......wha

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve: 12x^3 + 12x^2 - 9x = 0 I forgot how to factor when the first term has an exponent of 3... Here is what I have so far which isn't much. 3x(3x^2 + 3)(4x - 3)......wha      Log On


   

Question 790701: Solve: 12x^3 + 12x^2 - 9x = 0
I forgot how to factor when the first term has an exponent of 3...
Here is what I have so far which isn't much.
3x(3x^2 + 3)(4x - 3)......what do I do from here if this is even right.
Can I factor (3x^2 + 3) more? I know I'm supposed to have at least 3 answers for this problem.
Found 2 solutions by Alan3354, shosta:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve: 12x^3 + 12x^2 - 9x = 0
I forgot how to factor when the first term has an exponent of 3...
Here is what I have so far which isn't much.
3x(3x^2 + 3)(4x - 3)......what do I do from here if this is even right.
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12x^3 + 12x^2 - 9x = 0
Factor out 3x
3x*(4x^2 + 4x - 9) = 0
--> x = 0 ******** Solution #1
The trinomial can't be factored.
4x^2 + 4x - 9 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B4x%2B-9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A4%2A-9=160.

Discriminant d=160 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+160+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+160+%29%29%2F2%5C4+=+1.08113883008419
x%5B2%5D+=+%28-%284%29-sqrt%28+160+%29%29%2F2%5C4+=+-2.08113883008419

Quadratic expression 4x%5E2%2B4x%2B-9 can be factored:
4x%5E2%2B4x%2B-9+=+%28x-1.08113883008419%29%2A%28x--2.08113883008419%29
Again, the answer is: 1.08113883008419, -2.08113883008419. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B4%2Ax%2B-9+%29

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Can I factor (3x^2 + 3) more? I know I'm supposed to have at least 3 answers for this problem.

Answer by shosta(4) About Me  (Show Source):
You can put this solution on YOUR website!
12x^3 + 12x^2 - 9x = 0
okay so first, you were correct in your assumption that we could factor a 3x out, but the rest was incorrect
after we factor a 3x out of every term we are left with
3x+%284x%5E2%2B4x-3%29+=0 now, we ignore the 3x for now and focus on factoring the other terms
to factor 4x^2+4x-3 we look at the multiples of the first and last terms (4 and 3) and try to make them add or subtract to equal the middle term (4). Since out last term is negative this means our answer is going to involve subtraction and be in the form (#X - #)(#X + #).
so the factors of 4 are 1X4 2X2
the factors of 3 are 1X3
so we try to arrange these terms in a way that will give us back the same equation we had before when we multiply it out
+%282x-1%29%282x%2B3%29+
to check to make sure this is the correct order we can foil it out and make sure it matches the original, if not rearrange the terms and foil again
now don't forget to put the 3x back up there
so you have
+3x%282x-1%29%282x%2B3%29+