When f(x) is divided by (x-2) there is a remainder of k+7. If f(x)=2x^3 - 4x^2 + 3x + 1 , then find the value of 'k'.

Question

Not sure how to answer this, any help is much appreciated!!

Answer 1

By the Remainder Theorem, the remainder when f(x) is divided by x-2 is f(2).

 

Since f(2) = 7, we have k+7 = 7.

 

So, k = 0.

Answer 2

Use synthetic division (or long division).

Determine the remainder, set = k + 1, and solve for k.