College algebra
posted by Karlee on .
Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers.
f(x)=x^32x^213x10
x=

f(1) = 121310 ≠ 0
f(1) = 1  2 + 13 10 = 0 , so x+1 is a factor
by synthetic division
x^3  2x^2  13x  10 = (x+1)(x^2  3x  10)
= (x+1)(x5)(x+2) = 0 for roots
x = 1 or x = 2 or x = 5