Question

an unknown polynomial f(x) of degree 32 yields a remainder of 1 when divided by x-1 and a remainder of 3 when divided by x-3, find the remainder when f(x) is divided by (x-1)(x-3).

What is the answer? and i was wondering if the part about the polynomial being degree 32 is really relevant

Answer 1

the remainder will always have degree less than the divisor. So, it will be of the form r(x)=(ax+b)

So, you know that
r(1)=1
r(3)=3

Now solve for a and b.

As you surmised, the degree of p(x) does not really matter.