Question

P (x) =x⁴-3x²+kx-2, where I is an unknown integer. P (x) divided by (x-2) has a reminder of 10. What is the value of K?A) -2B) 2C) 4D) -4

Answer 1

Since (x-2) has a remainder of 1., we can also say that when x=2, P(X)=10. This because of a statement in the Polynomial remainder theorem.

Then, substituing x=2 and P(X)=10, we can isolate k:

$\begin{gathered} 10=2^4-3(2)^2+k(2)-2 \\ 10=4+k(2)-2 \\ 10=2+k(2) \\ 8=k(2) \\ k=\frac{8}{2}=4 \end{gathered}$