Question

what is the remainder of ((3x^3 - 5x^2 - 4x + 1) div (x + 3))?
113
-25
-113
25

Explanation:

Step1: Recall the Remainder Theorem

The Remainder Theorem states that if a polynomial \( f(x) \) is divided by \( (x - a) \), the remainder is \( f(a) \). In our case, the divisor is \( (x + 3) \), which can be written as \( (x - (-3)) \). So we need to find \( f(-3) \) where \( f(x)=3x^{3}-5x^{2}-4x + 1 \).

Step2: Substitute \( x=-3 \) into the polynomial

Substitute \( x = -3 \) into \( f(x) \):
\[

$$\begin{align*} f(-3)&=3(-3)^{3}-5(-3)^{2}-4(-3)+1\\ &=3(-27)-5(9)+12 + 1\\ &=-81-45 + 12+1\\ &=-126 + 13\\ &=-113 \end{align*}$$

\]

Answer:

-113