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 \(p(x)=0\): \(x-2=0 \Rightarrow x=2\). Remainder = \(f(2)\).

Step2: Calculate \(f(2)\)

Substitute \(x=2\) into \(f(x)\):
\(f(2) = -(2)^5 -3(2)^3 +2(2)^2 -80\)
\(= -32 -3(8) +2(4) -80\)
\(= -32 -24 +8 -80\)
\(= -104\)

Answer:

-104