just learned about the remainder theorem today and had to make this i'm not even gonna bother making fancy ui
no exponentiation here whatsoever EXAMPLE: Let P(x) = x^2 - 3x + 2, and we want to evaluate P(3). Dividing P(x) by (x - 3), we get: (x^2 - 3x + 2) / (x - 3) = x remainder 2 -> Q(x) = x and R = 2 The value of R is the value of P(3). This works for any polynomial and value. PROOF: Assume P(x) is our polynomial, and we want to find P(a). Consider the fact that P(x) can be divided by (x - a) to get Q(x) remainder R, where Q(x) is a polynomial. Thus, P(x) = (x - a)Q(x) + R. Plugging a into P(x), we get: P(a) = (a - a)Q(x) + R The Q(x) term vanishes, leaving only R as the value of P(a).
