what is the remainder when ( p(x) ) is divided by ( x - 1 )? ( p(x)=x^{3}-3x^{2}-10x + 24 )
a. 24
b. 12
c. 30
d. 0

Question

Accepted Answer

# Explanation:
## Step1: Recall the Remainder Theorem
The Remainder Theorem states that if a polynomial $ p(x) $ is divided by $ x - a $, the remainder is $ p(a) $. Here, we are dividing $ p(x)=x^{3}-3x^{2}-10x + 24 $ by $ x - 1 $, so $ a = 1 $.

## Step2: Substitute $ x = 1 $ into $ p(x) $
Calculate $ p(1) $ by substituting $ x = 1 $ into the polynomial:
$$
\begin{align*}
p(1)&=(1)^{3}-3(1)^{2}-10(1)+24\
&=1 - 3 - 10 + 24\
&=(1 + 24)-(3 + 10)\
&=25 - 13\
&=12
\end{align*}
$$

# Answer:
B. 12

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the Remainder Theorem

Step2: Substitute \( x = 1 \) into \( p(x) \)

Answer: