One factor of f (x) = 5x^3+5x^3+5x^2-170x+280

is (x + 7). What are all the roots of the function? Use the Remainder Theorem.

Since we know that (x+7) is a factor, and since we know all of the coefficients are divisble by 5, we can write a factorization as

... f (x) = 5 (x + 7) (x² - 6x + 8)

Evaluating f (2), we find that f (2) = 0, so 2 is another root and our factorization becomes ...

... f (x) = 5 (x + 7) (x - 2) (x - 4)

The roots of the function are x = {-7, 2, 4}.