Question

what is the remainder of (4x³ - 3x² - 4x + 2) ÷ (x - 3)? 71 145 -71

Explanation:

Step1: Apply Remainder Theorem

For polynomial $f(x)$ divided by $(x-a)$, remainder is $f(a)$. Here $a=3$, $f(x)=4x^3-3x^2-4x+2$.

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

$$f(3)=4(3)^3 - 3(3)^2 - 4(3) + 2$$

Step3: Calculate each term

$4(3)^3=4\times27=108$, $3(3)^2=3\times9=27$, $4(3)=12$

Step4: Compute final value

$$f(3)=108 - 27 - 12 + 2=71$$

Answer:

71