Question

divide and enter only the remainder!!! (numerator only)
\\(\frac{x^3 - x^2 - 6}{x + 2}\\)
note you will need to enter a 0x term for the missing power.
if image does not show: \\(x^3 - x^2 - 6\\) divided by \\(x + 2\\)

Explanation:

Step1: Use Remainder Theorem

The Remainder Theorem states that the remainder of dividing a polynomial \( f(x) \) by \( x - a \) is \( f(a) \). Here, we have \( x + 2 = x - (-2) \), so \( a = -2 \).
First, define the polynomial \( f(x)=x^{3}-x^{2}+0x - 6 \) (adding the missing \( 0x \) term).

Step2: Substitute \( x=-2 \) into \( f(x) \)

\[

$$\begin{align*} f(-2)&=(-2)^{3}-(-2)^{2}+0\times(-2)-6\\ &=-8 - 4+0 - 6\\ &=-12 - 6\\ &=-18 \end{align*}$$

\]

Answer:

\(-18\)