Use the Remainder Theorem, which says that the value for ** x** that makes the factor (in this case,

**) equal to 0 can be substituted into the function to yield the remainder (in this case, 6).**

*x–k*In this case, k is the value that makes ** x–k **have the value of 0. Thus, we will use

**as the value of**

*k***in the function or polynomial given and then set that equal to the remainder, which was given to us as 6.**

*x*f(x) = x^{3} + 2xk – 3k [original function given to us]

f(k) = k^{3} + 2(k)(k) – 3 k = 6 [original function with ** k** used as the value of

**and the function set equal to 6, the remainder]**

*x*k^{3} + 2k^{2} – 3k = 6

I decided that trial and error was my quickest way to find ** k**, but I'll let you find

**however you choose.**

*k*