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Proposition: For all polynomials p and q and all reals c and a:
cPoly[a] = c, x[a] = a, (p+q)[a] = p[a] +R q[a], (p*q)[a] = p[a] *R q[a].
When evaluating a polynomial p on a real a, we substitute aPoly for every occurrence of x in p and then use arithmetic on reals.
(x+1) = 2+1 = 3 (x*x+2*x+1) = 3*3+2*3+1 = 16