Instead of doing your homework for you, I'll do one exactly like yours step-by-step so you can use it as a model to do yours by.Given f(x)=x^3+kx-36, and x-3 is a factor
We divide f(x) by x-3, using synthetic division (be sure to change the sign of
-3 to +3 when using synthetic division).
3 | 1 0 k -36
| 3 9 3k+27
1 3 k+9 3k-9
The remainder 3k-9 must be 0, so 3k-9 = 0
3k = 9
k = 3
Edwin
The fact that (x+1) is a factor of the polynomial f(x) = x^3 + kx + 2, means that the value of -1
is the root of this polynomial: f(-1) = 0, due to the Remainder theorem.
So, we substitute x= -1 into the polynomial and equate it to zero
(-1)^3 + k*(-1) + 2 = 0.
It is an equation to determine the value of k. So, simplify and find k
-1 -k + 2 = 0
-1 + 2 = k
k = 1.
ANSWER. k = 1.