Question

How do you find a polynomial of degree three that when divided by x - 2 has a remainder of 3?

Answer 1

Multiply `(x-2)` by any quadratic and add `3`

e.g. `(x-2)x^2+3 = x^3-2x^2+3`

Explanation:

`(x-2)` multiplied by any quadratic will give a cubic.

If you then add `3`, that will be the remainder if you divide the resulting polynomial by `(x-2)`