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A polynomial puzzle in an olympiad is usually solved in two lines, if you know the trick. In this course you learn how to find a zero by testing a few numbers, and how to use an identity to avoid a long calculation. Then you solve problems and take a timed paper in the style of an olympiad.

What's inside

1. Skill: finding zeroes by testing a few numbers: To find the whole-number zeroes of a polynomial, list the divisors of the constant term, with both signs, and test each one. Once a zero is found, divide it out and factorise what is left. If the leading coefficient is not 1, a zero can be a fraction: its top divides the constant term and its bottom divides the leading coefficient.
2. Skill: identities that save a long calculation: Many long calculations are identities in disguise. Write a number near a round number as the round number plus or minus a small one, and the identities give the answer without a calculator. If a + b + c = 0, the sum of the cubes is 3abc. From x + 1/x you can find x² + 1/x² and x³ + 1/x³ without finding x.
3. Olympiad practice: the zeroes and the coefficients: The zeroes of a polynomial are tied to its coefficients. For a quadratic, the sum of the zeroes is minus b over a and their product is c over a. For a cubic there are three such rules. They check a factorisation, build a polynomial from its zeroes, and find expressions in the zeroes without finding the zeroes.