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Year 10A Patterns and Algebra (Polynomials (Introduction to Polynomials…
Year 10A Patterns and Algebra
Core Concepts
Existing Core Concepts
Long Division
Review
Expanding
Factorising
Polynomials
Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems (ACMNA266)
Introduction to Polynomials
leading term, constant term, leading coefficient (?), constant term, monic polynomial (?), degree
P(x)
what is a polynomial and degrees of polynomials (naming - constant, linear, quadratic, cubic, quartic, etc.)
Evaluating Polynomials
P(c) notation
Adding , Subtracting and Multiplying Polynomials
adding, subtracting & multiplying
Dividing Polynomials
to find the quotient and remainder, expressing the polynomial as the product of the linear expression and another polynomial plus a remainder, ie P(x)=(x−a)Q(x)+c
Remainder Theorem
Factor Theorem
Factorising Cubic Polynomials
Factorising Quartic Polynomials
Solving Polynomials
Activities
Problem Solving
What is a Polynomial?
Generalise from Quadratic
P(x), P(c) notation
Naming of Polynomials: Constant, Linear, quadratic, cubic, quartic etc
Maybe split Evaluating Polynomials to another lesson?
be able to recognise anx^n + a(n-1)x^(n-1) + ... + a1x + a0 as a polynomial
Leading Term and Coefficients
Constant term
Dividing by polynomials
Linear divisors only
Extension
Dividing by Quadratics
Applying Operations to Polynomials
Remainder theorem
factor theorem
factor theorem & roots