SOLUTION: Factoring Strategy-Factor Com[pletely Tutor, I am having trouble with tougher problems in factoring out completely. I need help from A to Z explaination for the following probl

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Question 371175: Factoring Strategy-Factor Com[pletely
Tutor,
I am having trouble with tougher problems in factoring out completely. I need help from A to Z explaination for the following problem. Thank you.
Here is my answer: 3x(x+2)(x-2)
what do you do if there are no x^2,or integer?
Problem: 3x^3-12x
Problem: 9x^2 + 4y^2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Factoring strategy:
  1. Always start with the Greats Common Factor (GCF). (If the GCF is 1, this step is optional.)
  2. After the GCF you try any or all of the other factoring techniques:
    • Factoring by patterns:
      • "Difference of squares" pattern: a%5E2-b%5E2+=+%28a%2Bb%29%28a-b%29
      • "Difference of cubes" pattern: a%5E3-b%5E3+=+%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29
      • "Sun of cubes" pattern: a%5E3%2Bb%5E3+=+%28a%2Bb%29%28a%5E2-ab%2Bb%5E2%29
      • "Perfect square trinomial" patterns:
        • a%5E2+%2B2ab+%2Bb%5E2+=+%28a%2Bb%29%28a%2Bb%29+=+%28a%2Bb%29%5E2
        • a%5E2+-2ab+%2Bb%5E2+=+%28a-b%29%28a-b%29+=+%28a-b%29%5E2
    • Trinomial factoring %28ax%5E2%2Bbx%2Bc%29
    • Factoring by grouping
    • Factoring by trial and error of the possible rational roots.

    There is no particular order to use with these techniques. However, the last two are often more difficult so many prefer to try the other two first. Also, the techniques can be used more than once on the same expression!

Let's see how this works.
Problem: 3x%5E3-12x
Start with the GCF (which in this case is 3x:
3x%28x%5E2-4%29
Next we try the other techniques. It takes practice to learn how to find the technique(s) that will work. In this expression, x%5E2-4 is a difference of squares so we can use that pattern:
3x(x+2)(x-2)

Problem: 9x%5E2+%2B+4y%5E2
First the GCF. The GCF here is 1. So we need not factor it out.
Then we look for another technique. This is a sum of squares but there is no pattern for "sum of squares"!
This expression has only two terms. This is too few for both trinomial factoring and factoring by grouping.
And the last techniques is used with expressions of one variable.
In other words, 9x%5E2+%2B+4y%5E2 does not factor (unless you use complex numbers).