Question

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.

Answer 1

x = –7, x = 2, or x = 4

Explanation:

Answer 2

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}.