4questions about the polynomial remainder theorem

None of these questions have anything to do directly with the polynomial remainder theorem. The theorem says that the remainder upon dividing a polynomial by is given by the value of .

For these questions, all you really have to do is evaluate the given polynomials at the given points, and IMO is much less work.

Question 2:

Question 3:

Question 4: Here you have check the value of and 2 and -2, then interpret them as points in the coordinate plane, .

Question 5: Same as in question 4, but you have to check at -4, -3, -2, -1.

- - -

If you insist on using the polynomial remainder theorem, it's a question of polynomial division. For instance, in question 2 you'd compute

so the remainder is 77, as we found by simply computing .

60%