MM Unit 1: TOPIC 2: Cubic and Quartic Polynomials

1 MM Unit 1: TOPIC 2: Cubic and Quartic Polynomials Learning Goals Students should be able to do and know: By hand: (these will be tested mainly in the non-calculator section of assessments) Determine the remainder when a polynomial is divided by a linear binomial Express a polynomial with integer co-efficients in the form = + Determine *(,),./ Solve Cubic and Quartic equations using appropriate techniques, including the null factor theorem draw graphs of Polynomials to degree 3 and degree 4 (when in factored form).. (not location of TPs for degree 3 and 4), showing intercepts Determine the rule for a Cubic or Quartic graph given key features Determine the domain and range of a relation using set and interval notation sketch the power functions y = xn ,n 3, 4 and simple transformations of these, showing key features How to identify a polynomial and the meaning of coefficient, degree that Cubic refers to a polynomial of degree 3 and Quartic to degree 4 How to use Pascal s Triangle to expand binomials to the power of n (where n is a natural number) that there are various forms of equations for Cubic and Quartic Polynomials (expanded form, factor form, power function form) that there are two graphical forms for Polynomials with degree 3.

2 The one when the equation can be written in power function form (ie y = a (x b)n + c ) and the one when it cannot Expand a product of 3 linear factors how to factorise Cubic and Quartic expressions using various techniques including factor theorem, sum and difference of 2 cubes, substitution that not all Cubic Polynomials can be factorised that, for those that can, the constants in the factor brackets must multiply to give the constant term in the expanded form Factor, Remainder and Rational Root theorems How to use the bisection method to determine and verify solutions to equations over a specified interval that finding the values of x that makes each factor bracket zero gives the values of x for which the polynomial has a value of zero that there is relationship between factors and x-intercepts of the related graph including the significance of repeated factors that the domain is the set of x values permissible in a situation for the independent variable that the range is the set of y values permissible for the dependent variable that the maximal domain as the default domain if one isn t given OTHER RESOURCES Online text: Website resource on zeros and roots: Website resource on solving equations : More formal language but still quite a good resource: (1) Alternative method of factorising