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

7). What are all the roots of the function? Use the Remainder Theorem.

x = - 4, x = - 2, or x = 7

x = - 7, x = 2, or x = 4

x = - 7, x = 5, or x = 280

x = - 280, x = - 5, or x = 7

We will use the Reminder Theorem:

(5 x³ + 5 x² - 170 x + 280) : (x - 7) = 5 x² - 30 x + 40

5 x² - 30 x + 40 = 5 (x² - 6 x + 8)

f (2) = 4 - 12 + 8 = 0

(x² - 6 x + 40) : (x - 2) = x - 4

Finally: 5 x³ + 5 x² - 170 x + 280 = 5 (x + 7) (x - 2) (x + 4)

Answer: B) x = - 7, x = 2, or x = 4.