MagicMath: Polynomial Evaluation

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Polynomial Evaluation

If you have a polynomial P(x) and you like to see the value of P(x) at the point x = a, you can do it easily here. Suppose you have an equation

P(x) = 0 and you have obtain a solution x = r. Then you can check your solution by evaluating P(r).

Enter a P(X) to be evaluated in infix form
(x^2 + 1) * (7*X - 1) + 17
or
(5*x^2 + 4*x +3)

Note * (shift-8) is for multiplication and ^ (shift-6) is for powering.

P(x): X =
Challenge:
Do you know that if you divide P(x) by a linear polynomial x - a, the remainder you get is always P(a)?
Can you prove this fact?

algebra