Make sure all solutions are in lowest terms. 5/6 • 1/3
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In order to factor a polynomial , we have to find all its roots
so that we can rewrite the polynomial as
This is exactly the same idea we apply when we factor numbers: we look for all the primes that divide the number, and then we write
When talking about polynomials, the idea of prime numbers is represented by irreducible polynomials, i.e. polynomials with no roots.
So, we have to find a root of our polynomial. Using the rational root theorem, we can check that is a solution:
So, our polynomial is divisible by . The long division yields
Which is the same as
We can complete the factorization by breaking the quadratic equation: using the standard quadratic formula we can find the solutions
Which implies
And finally