Question

How do I find all possible rational zeros in a polynomial function?f(x) = x^4-2x^3-4x^2+2x+3

Answer 1

The factors are 1 , -1 twice and 3

Here, we want to find the rational roots of;

$f(x)\text{= }x^4-2x^3-4x^2+2x+3$

We can start here by trying out simple numbers if we cannot factorize the polynomial at a go

The given polynomial here can be factorized

We can express it as;

$x^4-2x^3-4x^2+2x+3\text{ = (}x-1)(x+1)^2(x-3)$

So what we have here is to simply equate individual linear factor to zero

Thus, we have the factors as;

1 , -1 twice and 3