Question

What is the value of k if 2x3 − 4x2 + kx − 3 is divided by x − 1 and gives a remainder of 3?

Answer 1

To find the value of k if 2x3 − 4x2 + kx − 3 is divided by x − 1 and gives a remainder of 3:

$y=2x^3-4x^2+kx-3$

Using remainder theorem

$\begin{gathered} x-1=0 \\ x=1 \\ f(x)=3,\text{ when x = 1} \end{gathered}$

$\begin{gathered} 2x^3-4x^2+kx-3 \\ 2(1)^3-4(1)^2+k(1)-3=3 \\ 2-4+k-3=3 \\ -2-3+k=3 \\ -5+k=3 \\ k=3+5 \\ k=8 \end{gathered}$

Therefore the value of k = 8

Hence the correct value of k is Option B