Question

(2x³ + 3x² + kx - 2) ÷ (x + 1)
Remainder should be 5.

Answer 1

Let f(x)=2x3+3x2−kx+5

By remainder theorem, when f(x) is divided by (x−2)

x−2=0,⇒x=2

the remainder =f(2)

=2(2)3+3(2)2−k(2)+5

=16+12−2k+5

=33−2k

According to question 

33−2k=7

⇒2k=26

⇒k=13