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}.

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