Question

what the remainder after $x^3 - 2x^2 - 5x + 6$ is divided by $x - 3$

Explanation:

Step1: Apply Remainder Theorem

For polynomial $f(x)$, remainder when divided by $x-a$ is $f(a)$. Here $a=3$.

Step2: Substitute $x=3$ into $f(x)$

$f(x)=x^3-2x^2-5x+6$
$f(3)=3^3 - 2(3)^2 -5(3)+6$

Step3: Calculate each term

$3^3=27$, $2(3)^2=18$, $5(3)=15$

Step4: Compute final value

$f(3)=27-18-15+6=0$

Answer:

0