Use the rationals theorem to find all the zeros of the polynomial function. Use the zeros to factor f over the real numbers.

Question

f(x)=x^3-2x^2-13x-10
x=

Answer 1

f(1) = 1-2-13-10 ≠ 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)(x-5)(x+2) = 0 for roots

x = -1 or x = -2 or x = 5