what is the remainder of (3x³ -5x² -4x +1) ÷ (x + 3)?

Explanation:

Step1: Apply Remainder Theorem

Set $x + 3 = 0$, so $x = -3$. Substitute $x=-3$ into $3x^3 -5x^2 -4x +1$.

Step2: Calculate each term

$3(-3)^3 = 3(-27) = -81$ $-5(-3)^2 = -5(9) = -45$ $-4(-3) = 12$ The constant term is $1$.

Step3: Sum all terms

$\text{Total} = -81 -45 +12 +1$

Answer:

-113