SOLUTION: When x^4 +kx^3 +1 is ÷ by x-1 the remainder is 2. Find K. Can you show me the steps for finding K? Thank you!

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Question 1040816: When x^4 +kx^3 +1 is ÷ by x-1 the remainder is 2. Find K.
Can you show me the steps for finding K? Thank you!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Using the remainder theorem, the idea is that plugging in x = 1 will lead to a result of 2. We need to find the value of k that makes this happen.

f%28x%29+=+x%5E4%2Bk%2Ax%5E3%2B1
f%281%29+=+%281%29%5E4%2Bk%2A%281%29%5E3%2B1 Replace every x with 1
f%281%29+=+1%2Bk%2A%281%29%2B1
f%281%29+=+1%2Bk%2B1
2+=+1%2Bk%2B1 Replace f(1) with 2. Since we want the remainder to be 2.

Let's solve for k

2+=+1%2Bk%2B1
2+=+k%2B2
k%2B2+=+2
k%2B2-2+=+2-2
k+=+0

So the final answer is k+=+0