Question

Given that f(x)=x^3+kx^2-2x+1 has reamainder k when it is divided by (x-k),find possible values of k
@Callisto

Answer 1

Use the remainder theorem. When f(x) is divided by x=m and have a remainder n, we have
f(m) = n
In this case, f(x) is divided by k and the remainder is k, so, what is m and n?

Answer 2

f(k)=k

Answer 3

k^3+k(k)^2-2k+1=k
k^3+k^3-3k+1=0
2k^3-3k+1=0
like this @Callisto

Answer 4

Yes. Now, try factor theorem to factorize the expression on the left.

Answer 5

nt sure..

Answer 6

By educated guess, try x=1...

Answer 7

f(1)=k

Answer 8

Sorry... Consider f(k) = 2k^3-3k+1, what is f(1)?

Answer 9

, try x=1..

Answer 10

Ehmmmm....
If g(k) = 2k^3-3k+1, what is g(1)?

Answer 11

g(1)=0
so, (x-1) is a factor of g(k)

Answer 12

(k-1) is a factor of g(k), there is no x in the function g.
Now, divide g(k) by k-1 to get the other factor. Can you do it?

Answer 13

not sure..