Factoring Polynomial using Quadratic Equation
I'm trying to use the quadratic equation (QE) to factor a degree 2 polynomial into the format: , where a is any real number.
This works great for equations like:
The QE gives roots , and .
This approach fails for other polynomials such as:
The roots found with the QE are . But .
9 is the GCF from the coefficients of (2), so (2) can be rewritten as:
and by using the QE on the second term, this equals:
. And (2), so this seems to be a better approach.
So my question is: must the input to QF be a polynomial that has coefficients with , for the result to give roots that can be used to reconstruct the original function?