Question

question
if $f(x) = x^2 - 5$, then what is the remainder when $f(x)$ is divided by $x + 2$?

Explanation:

Step1: Recall Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( x - a \), the remainder is \( f(a) \). Here, we are dividing by \( x + 2 \), which can be written as \( x - (-2) \), so \( a=-2 \).

Step2: Evaluate \( f(-2) \)

Given \( f(x)=x^{2}-5 \), substitute \( x = -2 \) into the function:
\( f(-2)=(-2)^{2}-5 \)
First, calculate \( (-2)^{2}=4 \), then \( 4 - 5=-1 \).

Answer:

The remainder is \(-1\).