SOLUTION: factor 9x^2+3x-2

Question 23858: factor
9x^2+3x-2
Answer by PeterC(8) (Show Source): You can put this solution on YOUR website!
A quadratic funtion can be factored as ,
where r1 and r2 are the roots (solutions) to the equation .
We can find r1 and r2, using the quadratic formula
.
Here,
and

Therefore, our factors are:
What I have shown (creating a factored expression by finding the roots of a polynomial equation) is a brute-force method that will always work. However, you can often solve the problem by examination, by posing the question, "What are two numbers whose sum is b/a and product is c/a?" (It is a bit easier to do this if a = 1.) In fact, the usual reason for factoring a quadratic expression is that it gives us a shortcut to finding its roots (which are the negatives of those two numbers). If we can recognize the numbers that create our desired sum and product, we can avoid a somewhat laborious computation with the quadratic formula.
In this problem,

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