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: