Question

When $x^3+2x^2-kx+4$ is divided by x -2, the remainder is k. The the value of k is ______.

• A. 4
• B. -4
• C. $6\frac{2}{3}$
• D. -$6\frac{2}{3}$

Answer 1

The correct option is C $6\frac{2}{3}$

Given that when $x^3+2x^2-kx+4$ is divided by x -2, the remainder is k. That means when x = 2 is substituted in the expression , it will be equal to k.
$(2{)}^3+2(2{)}^2-2k+4=k$
8 + 8 - 2k + 4 = k
3k = 20
$\therefore k=6\frac{2}{3}$