Key Points
1. A polynomial in x has terms in positive integer powers of x, and may also have a constant term.

2. The order of a polynomial in x is the highest power of x which appears in the polynomial.

3. The factor theorem states that if (x - a) is a factor of a polynomial f(x) then f(a) = 0 and x = a is a root of the equation f(x) = 0. Conversely if f(a) = 0, then x - a is a factor of f(x).

4. The remainder theorem states that f(a) is the remainder when f(x) is divided by (x - a).

5. The curve of a polynomial function of order n has up to (n - 1) turning points.

6. The behaviour of the curve of a polynomial of order n, for large positive and negative values of n, depends on whether n is even or odd, and whether the coefficient of the term in xb is positive or negative.

7. The vertex and line of symmetry of a quadratic may be found by complex the square.

8. Translations of the graph of the function y = f(x):

Translation           Resulting Function
(t0)           y = f(x - t)
(0s)           y = f(x) + s
(ts)           y = f(x - t) + s


9. Binomial coefficients, denoted by nCr or (n r) can be found:
• using Pascal's triangle
• using tables
• using the formula nCr = n! ⁄ r!(n - r)!

10. The binomial expansion of (1 + x)n may also be written:

(1 + x)n = 1 + nx + n(n - 1) ⁄ 2! x2 + n(n - 1)(n - 2) ⁄ 3!x3 + ... + nxn-1 + xn

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