Question

numeric 1 point what is the remainder when $x^6 - 5$ is divided by $(x + 3)$? answer

Explanation:

Step1: Recall the Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( (x - a) \), the remainder is \( f(a) \). For the divisor \( (x + 3) \), we can rewrite it as \( (x - (-3)) \), so \( a=-3 \).

Step2: Define the polynomial and substitute \( a=-3 \)

Let \( f(x)=x^{6}-5 \). We need to find \( f(-3) \). Substitute \( x = -3 \) into the polynomial:
\[

$$\begin{align*} f(-3)&=(-3)^{6}-5\\ &=729 - 5\\ &= 724 \end{align*}$$

\]

Answer:

724