Use the real zeros to factor f x^4 plus 10^3 minus 20x^2 minus 90x plus 99

f (x) = (x + 11) (x + 3) (x - 1) (x - 3)

Step-by-step explanation:

f (x) = x⁴ + 10x³ - 20x² - 90x + 99

f (x) is a fourth order polynomial, so it has 4 roots. Use rational root theorem to find possible rational roots.

±99, ±11, ±9, ±3, ±1

By trial and error, the zeros are - 11, - 3, 1, and 3.

f (x) = (x + 11) (x + 3) (x - 1) (x - 3)