Question

Determine if (x+1) and (x-1) are factors of f(x)=3x - x? +2x-4.

Answer 1

The given function is

`f(x)=3x^5-x^2+2x-4`

To determine if the given factors are solutions or roots, we have to evaluate the function when x = 1, and x = -1. If the evaluation gives zero, then those factors are correct.

`\begin{gathered} f(1)=3(1)^5-(1)^2+2(1)-4=3-1+2-4=5-5=0 \\ f(-1)=3(-1)^5-(-1)^2+2(-1)-4=-3-1-2-4=-10 \end{gathered}`

Hence, (x-1) is factor of f(x) while (x+1) is not.