Question

Which of the following is a root of the polynomial shown below?

f(x)= x^3 + 2x^2 - x - 2

A. 3
B. 0
C. 1
D. 2

Answer 1

The roots for it are,
x=-2
x=-1
x=1

Answer 2

Use the factor theorem which means finding

f(3), f(0) f(1) and f(2) if any of them are equal to zero then that value is a factor and hence a root.

This method eliminates the need to solve the polynomial..

so using the answers shown above where you are told x = -1 is a solution


f(-1) = (-1)^3 + 2(-1)^2 -(-1) - 2

f(-1) = 0 which means (x + 1) is a factor and x = -1 is a zero or root.