- Mathematical Methods
- Year 11
Polynomials
approx. 9 hrs
6 topics
18 concepts
Deepen your understanding of Polynomials to optimise your performance in Mathematics.
approx. 9 hrs
6 topics
18 concepts
Deepen your understanding of Polynomials to optimise your performance in Mathematics.
Year 11 Mathematical Methods gives students the essential skills associated with Polynomials as specified in the Senior Mathematics Australian curriculum. In this program, we help students build on their prior learning to develop algebraic skills to manipulate polynomials and find rational factors. Also, students will learn how to apply the rational-root theorem to find all possible rational roots. This enables them to fully factorise any given polynomial. In addition, we show students how to sketch polynomials using the rational factors.
This learning program is made up of the following 6 topics, broken down into 18 concepts.
Apply the rational-root theorem to find rational factors of a given polynomial
Factorise a polynomial using the factor theorem or the rational-root theorem
Root-coefficient relationships for quartic equations
Root-coefficient relationships for cubic equations
Approximate solutions of equations through an iterative process
Approximate solutions of equations by halving the interval
Approximate solutions of equations using Newton's method
Equating coefficients of a polynomial
Applications of the remainder or factor theorem
Use given data to find the roots of a polynomial
Verify the remainder theorem and use it to find factors
Use the factor theorem and long division to find all zeroes of a polynomial
Sketch polynomials with degree no more than four by using the leading term, the roots and theÂ x-Â andÂ y-intercepts
Determine the effect of single, double and triple roots of a polynomial equation on the shape of the graph
Add and subtract polynomials and multiply polynomials by linear expressions
Division of polynomials
State the degree of a polynomial after adding, subtracting, multiplying or dividing of one or more polynomials
Identify a polynomial expression and describe the key features using appropriate terminology
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