Answer: 8
Step-by-step explanation
We use the remainder theorem here.
The remainder theorem is this:
If p(x) is divided over x-k, then p(k) is the remainder.
Compare x-2 to x-k to find that k = 2. Plug this into the function and set it equal to 22 so we can find k.
p(x) = x^5 - 3x^3 + 5x^2 - 7x + k
p(2) = (2)^5 - 3(2)^3 + 5(2)^2 - 7(2) + k
p(2) = 14 + k
p(2) = 22 because of the remainder theorem
14+k = 22
k = 22-14
k = 8
Therefore, when we divide (x^5 - 3x^3 + 5x^2 - 7x + 8) over (x-2), we'll get some quotient and a remainder of 22.