Question

Taking a pretest and am very confused, please help !

Answer 1

Option 4: f(2) ≠ 0, the binomial x-2 is not a factor of f(x).

Explanation:

Given the polynomial function:

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

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).

`\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}`

Since f(2) is not equal to 0, the binomial x-2 is not a factor of f(x).

The last option is correct.