SOLUTION: Explain how the quadratic formula can be used to factor a quadratic polynomial into two binomials using this equation. I am not so interested in the solution as I am interested in

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Question 147227: Explain how the quadratic formula can be used to factor a quadratic polynomial into two binomials using this equation. I am not so interested in the solution as I am interested in the explanation of the steps in factoring this equation into two binomials.
5x² + 8x + 3.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
It turns out that the solutions to any quadratic will form the factors of the quadratic itself. So let's say that we want to factor x%5E2%2B5x%2B6. We know that this factors to %28x%2B3%29%28x%2B2%29. But if we didn't know that, we can use the quadratic formula to find the solutions x=-3 and x=-2. From there, we need to get all terms to one side to get x%2B3=0 and x%2B2=0. Now just combine the two equations into one like this %28x%2B3%29%28x%2B2%29=0 (note: this is using the zero product property in reverse).