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