Is it possible to factor #y=2x^2 + 9x - 5 #? If so, what are the factors?
As it so happens, any quadratic can be factored into the form
That big block comes from the quadratic formula, along with the fact that given a polynomial
However, sometimes (when
If we have the factorization
then expanding the left hand side and comparing coefficients gives us the system
If we limit ourselves to integer solutions, then we quickly see from the first and third equations that
is a solution. Thus, substituting back, we have