24 multiple choice 1 point\nwhat is the remainder of $p(x)=x^4+x^3-x^2-2$ is divided by $x-3$?\n$-26$\n$43$\n…

24 multiple choice 1 point\nwhat is the remainder of $p(x)=x^4+x^3-x^2-2$ is divided by $x-3$?\n$-26$\n$43$\n$-17$\n$97$

24 multiple choice 1 point\nwhat is the remainder of $p(x)=x^4+x^3-x^2-2$ is divided by $x-3$?\n$-26$\n$43$\n$-17$\n$97$

Answer

Explanation:

Step1: Apply Remainder Theorem

For polynomial $p(x)$ divided by $x-a$, remainder is $p(a)$. Here $a=3$, so calculate $p(3)$.

Step2: Substitute $x=3$ into $p(x)$

$$p(3) = 3^4 + 3^3 - 3^2 - 2$$

Step3: Compute each term

$3^4=81$, $3^3=27$, $3^2=9$ $$p(3)=81+27-9-2$$

Step4: Calculate final value

$$p(3)=108-11=97$$

Answer:

D. 97