Foolproof method for simplifying polynomials with four terms?

When simplifying quadratic equations you have two options:

• factoring (which may or may not work)
• or the quadratic formula (which will always find the answer)

For quadrinomials what is the go to method?
For example if you try to factor this polynomial

$x^3 + 2x^2 + x - 4$

You would end up with:

$x^2(x + 2) + 1(x - 4)$

There must be a different method to solve this equation. Is there a quadrinomial equivalent to the quadratic formula?

Solution 1:

We put $f(x) = x^3+2x^2 +x-4$

we can see$: f(1)=0$ $ \Rightarrow$ $ f(x) $ is divisible by$ (x-1)$

After division :

$f(x) = (x-1)(x^2 +3x+4 )$