SOLUTION: Hello I have no idea how the instructor is coming up with 238 on the answer key. The problem is; Use the Remainder theorem to evaluate T(x)=3x^4-x^2 + 4, when x=-3. He does not gi

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Question 926699: Hello
I have no idea how the instructor is coming up with 238 on the answer key. The problem is; Use the Remainder theorem to evaluate T(x)=3x^4-x^2 + 4, when x=-3. He does not give a lesson this. The lesson he gave is P(x) etc, etc..., there is no T(x) in our book or in his lessons. There are going to be more of these on the test. What is the T(x) and how do I do it?
Found 2 solutions by EMStelley, MathLover1:
Answer by EMStelley(208) (Show Source):
You can put this solution on YOUR website!
The remainder theorem states that when you divide a polynomial by a linear expression such as x-c, the remainder is equal to the original polynomial evaluated at c. So in this example, the remainder theorem would state that when we divide by (add 3 to both sides in the equation x=-3), the remainder will be T(-3). The letters P(x) are not specific - they can be anything, in this case they are T(x). So, all we need to do is which is 238.

Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

to evaluate when just substitute for in

............

What is the T(x)? It is just symbol for a function (a functional symbol), you can name it how do you want.
T(x), or P(x), or f(x), or g(x), are used to name a functions, all are same as ; recall
you can use any functional symbol from above:
so, is same as ,, , or