Polynomials (Path)
Mathematics K–10 (2022) · Stage 5 · View this focus area on the NESA NSW Curriculum website ↗
Outcomes
MA5-POL-P-01 defines, operates with and graphs polynomials and applies the factor and remainder theorems to solve problems (Path: Adv, Ext)Content dot points
Each dot point has its own page with resources matched to it.
Define and operate with polynomials
- Recognise a polynomial expression a_nxⁿ + a_n - 1x^(n - 1) + … + a_2x² + a_1x + a_0 where n = 0,1,2… and a_0,a_1,a_2,…,a_n are real numbers 1 resource · 1 interactive/game
- Describe polynomials using terms such as degree, leading term, coefficient and leading coefficient, constant term, monic and non-monic 3 resources · 1 interactive/game
- Define a monic polynomial as having a leading coefficient of one
- Apply the notation P(x) for polynomials and P(c) to indicate the value of P(x) for x = c
- Add, subtract and multiply polynomials 2 resources
Divide polynomials
- Identify the dividend, divisor, quotient and remainder in numerical division
- Divide a polynomial by a linear polynomial to find the quotient and remainder 3 resources · 1 interactive/game
- Express a polynomial in the form P(x) = D(x)Q(x) + R(x), where D(x) is the divisor, Q(x) is the quotient and R(x) is the remainder 1 resource · 1 interactive/game
Apply the factor and remainder theorems to solve problems
- Verify the remainder theorem and use it to find factors of polynomials and solve related problems 2 resources · 1 interactive/game
- Develop and apply the factor theorem to factorise particular polynomials completely and solve related problems 2 resources · 1 interactive/game
- Apply the factor theorem and division to find the zeroes of a polynomial P(x) and solve P(x) = 0 (degree ≤ 4) 1 resource
- State the maximum number of zeroes a polynomial of degree n can have
Graph polynomials
- Graph polynomials in factored form
- Graph quadratic, cubic and quartic polynomials by factorising and finding the zeroes 1 resource
- Relate the term zeroes to polynomial functions and roots to polynomial equations
- Use graphing applications to determine the effect of single, double and triple roots of a polynomial equation P(x) = 0 on the shape of the graph for y = P(x) 2 resources · 2 interactive/game
- Graph polynomials using the sign of the leading term and the multiplicity of roots for the equation P(x) = 0 1 resource
- Use graphing applications to compare the graphs of y = - P(x), y = P(- x), y = P(x) + c and y = kP(x) to the graph of y = P(x) 2 resources · 2 interactive/game
Stage 5 planning resources
Stage- or course-wide documents (scope and sequences, guides) that cover this focus area alongside others.
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 03)
- Unit/PlanningSample scope and sequence: Stages 4–5 core and selected paths (NESA no. 04)
- Unit/PlanningSample scope and sequence: Stage 5 core and all paths (NESA no. 05)
- Unit/PlanningSample scope and sequence: Stage 5 core (NESA no. 02)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 06)
- Unit/PlanningSample scope and sequence: Stage 5 core and selected paths (NESA no. 01)
- Unit/PlanningSample scope and sequence: Stages 4–5 stage based (NESA no. 08)
- Unit/PlanningStage 5 – sample scope and sequence
- Unit/PlanningStage 5 – stage based – sample scope and sequence