Polynomials

Polynomials

1. The factor theorem:

   • If (x-a) is a factor of f(x) then f(a)=0 and x=a is a root of f(x)=0.

2. The remainder theorem:

   • f(a) is the remainder when f(x) is divided by (x-a).

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

4. 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 xᶯ is positive or negative.

5. The vertex and line of symmetry of a quadratic may be found by competing the square.

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

   • t 0
     • y=f(x-t)
   • 0 s
     • y=f(x)+s
   • t s
     • y=f(x-t)+s

7. Binomial coefficients can be found using Pascal's triangle.