Question

question
consider this polynomial function.
p(x) = x³ + 7x² - 4x - 28
what is the remainder when p(x) is divided by each of
type the answer in each box. use numerals instead of

x - 3:

x + 4:

Explanation:

Step1: Recall Remainder Theorem

The Remainder Theorem states that if a polynomial \( p(x) \) is divided by \( x - a \), the remainder is \( p(a) \).

Step2: Find remainder for \( x - 3 \)

For \( x - 3 \), \( a = 3 \). Substitute \( x = 3 \) into \( p(x) \):

$$
LATEXBLOCK0
$$

Step3: Find remainder for \( x + 4 \)

For \( x + 4 \), rewrite as \( x - (-4) \), so \( a = -4 \). Substitute \( x = -4 \) into \( p(x) \):

$$
LATEXBLOCK1
$$

Answer:

For \( x - 3 \): \( 50 \)
For \( x + 4 \): \( 36 \)