Answer:
Option 4: f(2) ≠ 0, the binomial x-2 is not a factor of f(x).
Explanation:
Given the polynomial function:
[tex]f(x)=2x^3+x^2-5x+2[/tex]
We want to determine if x-2 is a factor of f(x) using the factor theorem.
By the Factor Theorem:
So, to check if x-2 is a factor of f(x), we first need to evaluate f(2).
[tex]\begin{gathered} f(x)=2x^{3}+x^{2}-5x+2 \\ f(2)=2(2)^3+(2)^2-5(2)+2 \\ =2(8)+4-10+2 \\ =16+4+2-10 \\ f(2)=12 \end{gathered}[/tex]
Since f(2) is not equal to 0, the binomial x-2 is not a factor of f(x).
The last option is correct.
