ANSWER:
3rd option: -14
STEP-BY-STEP EXPLANATION:
We have the following polynomial:
[tex]3x^4\:-\:5x^2\:-\:20x\:+\:8[/tex]
If we divide it by (x - 1) we apply the remainder theorem, which consists of substituting the value in this case of 1 in the polynomial to determine the remainder, just like this:
[tex]\begin{gathered} x-1=0\rightarrow x=1 \\ \\ 3\left(1\right)^4\:-\:5\left(1\right)^2\:-\:20\left(1\right)\:+\:8 \\ \\ 3\cdot\:1-5\cdot\:1-20\cdot1+8 \\ \\ 3-5-20+8=-14 \end{gathered}[/tex]
So the correct answer is 3rd option: -14
