Question

suppose f(x) = -x⁵ - 3x³ + 2x² - 80 and p(x) = x - 2. what is the remainder when f(x) is divided by p(x)? type your answer in the boxes:

Explanation:

Step1: Apply Remainder Theorem

Set \( p(x)=x-2=0 \), so \( x=2 \). The remainder is \( f(2) \).

Step2: Calculate \( f(2) \)

Substitute \( x=2 \) into \( f(x) \):
\( f(2)=-(2)^5 - 3(2)^3 + 2(2)^2 - 80 \)
\( = -32 - 24 + 8 - 80 \)
\( = -96 \)

Answer:

-96