# Is it possible to factor #y=2x^2 + 9x - 5 #? If so, what are the factors?

##### 1 Answer

#### Explanation:

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