Polynomials

WhisperedWishes
Mind Map by WhisperedWishes, updated more than 1 year ago
WhisperedWishes
Created by WhisperedWishes almost 7 years ago
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A-Levels Maths (Core 1) Mind Map on Polynomials, created by WhisperedWishes on 05/12/2013.
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Polynomials
1 The factor theorem:
1.1 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:
2.1 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):
6.1 t 0
6.1.1 y=f(x-t)
6.2 0 s
6.2.1 y=f(x)+s
6.3 t s
6.3.1 y=f(x-t)+s
7 Binomial coefficients can be found using Pascal's triangle.
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