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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