Ch. 3 Polynomial Functions 

3.1 Characteristics of Polynomial Functions

Focus on

-          Identifying polynomial functions

-          Analysing polynomial functions

 End behaviour – the behaviour of the y-values of a function as |x| becomes very large

 Polynomial function – a function of the form f(x) = axn + an+1xn+1 + an+2xn+2 + … + a1+x +a0 where:

-          n is a whole number

-          x is a variable

-          The coefficients an to a0 are real numbers

Examples:

         f(x) = 2x-1

         f(x) = x2 + x -6

         y=x3 + 2x2 – 5x – 6

3.2  The Remainder Theorem

Focus on

-          Describing the relationship between polynomial long division and synthetic division

-          Dividing polynomials by binomials of the form x-a using long division or synthetic division

-          Explaining the relationship between the remainder when a polynomial is divided by a binomials of the form x-a and the value of the polynomial at x=0

3.3  The Factor Theorem

Focus on

-          Factoring polynomial

-          Explaining the relationship between the linear factors of a polynomial expression and the zeros of the corresponding functions

-          Modelling and solving problems involving polynomial functions

 Factor theorem – a polynomial in x, P(x), has a factor x-a if and only if P(a) = 0

3.4  Equations and Graphs of Polynomial Functions

Focus on

-          Describing the relationship between zeros roots and x-intercepts of polynomial functions and equations

-          Sketching the graph of a polynomial function without technology.

-      Modelling and solving problems involving polynomial functions