# How do you factor #x^4 - x^3 - 5x^2 - x - 6#?

##### 1 Answer

Using the Rational Zeros Theorem the solution is

#### Explanation:

If you have a polynomial with integer coefficients you can try to find the solutions applying the Rational Zeros Theorem.

This theorem says that if a root is rational, it has to have the numerator as one of the factors of the constant and the denominator as one of the factors of the coefficient of the leading term.

It is easier to see in your case.

First of all your polynomial has the coefficients integers, they are

The coefficient of the leading term is

The constant term is

The theorem tells us that if a rational root exists it must be one of this

Then we try all of them and see if we obtain zero

We were lucky and we found two roots,

Then we can start our factorization as

The part that is missing is the quadratic polynomial

If we multiply the terms we have

if we compare this with the initial polynomial

we have

Then the final factorization is

If you want to factorize in the complex numbers you can write