Algebra ii question. explain your answer.

First, we could try to factorize the polynomial. We could group the first and third terms, and the second and fourth term:



Now, x(x^2-9) is a common factor:

.

By the difference of squares formula, our final factorization is :

x(3x-1)(x-3)(x+3).

Here we can see clearly that the roots of f(x) are 0, 1/3, 3, and -3.

Remark: we grouped the terms in pairs as we did, noticing that the ratio of the exponents, and coefficient in each pair was the same. 

0, 1/3, 3, and -3.