Question

question: the remainder of f(x) divided by (x+3) is: * dividing f(x)=3x^3 +5x -10 by x+3 gives a remainder of 3x^2-9x-32 -106 x+3 106 none of these all of the other options (except none of these options) -96 96 3x^2-9x+32 skip this question x -3

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 \( x + 3 \), we can write it as \( x - (-3) \), so \( a=-3 \).

Step2: Substitute \( x = -3 \) into \( f(x) \)

Given \( f(x)=3x^{3}+5x - 10 \), substitute \( x=-3 \):
\[

$$\begin{align*} f(-3)&=3(-3)^{3}+5(-3)-10\\ &=3(-27)+(-15)-10\\ &=-81 - 15 - 10\\ &=-106 \end{align*}$$

\]

Answer:

-106 (corresponding to the option with -106)