| Manifesto | Bookstore | Contents | Amazon store | Term index | What changed? | Contact | Recommend |
Third Millennium International Mathematical Olympiad 2009
|
| The derivatives of two polynomials P(x) and Q(x) are divisible by x2009. Prove that the same is true of the derivative of their product. |
Copyright © 1996-2010 Alexander Bogomolny
Let P'(x) = p(x) x2009 and Q'(x) = q(x) x2009. Then
| (PQ)' | = P'Q + PQ' | |
| = px2009 Q + Pq x2009 | ||
| = x2009(pQ + Pq). |
Which proves the assertion.
Copyright © 1996-2010 Alexander Bogomolny
| 35678918 |  |
