Question

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

Explanation:

Step1: Identify root of divisor

For $x+3=0$, solve for $x$: $x=-3$

Step2: Apply Remainder Theorem

Substitute $x=-3$ into $3x^3-5x^2-4x+1$:
$$3(-3)^3 -5(-3)^2 -4(-3)+1$$

Step3: Calculate each term

$3(-27) = -81$, $-5(9)=-45$, $-4(-3)=12$, constant term $=1$

Step4: Sum all terms

$-81 -45 +12 +1 = -113$

Answer:

-113