Polynomials

Description

A-Levels Maths (Core 1) Mind Map on Polynomials, created by WhisperedWishes on 12/05/2013.
WhisperedWishes
Mind Map by WhisperedWishes, updated more than 1 year ago
WhisperedWishes
Created by WhisperedWishes over 11 years ago
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Resource summary

Polynomials
  1. The factor theorem:
    1. 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:
      1. f(a) is the remainder when f(x) is divided by (x-a).
      2. The curve of a polynomial function of order n has up to (n-1) turning points.
        1. 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.
          1. The vertex and line of symmetry of a quadratic may be found by competing the square.
            1. Translations of the graph of the function y=f(x):
              1. t 0
                1. y=f(x-t)
                2. 0 s
                  1. y=f(x)+s
                  2. t s
                    1. y=f(x-t)+s
                  3. Binomial coefficients can be found using Pascal's triangle.
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