The principal focus of polynomials is to explore the behaviour of polynomials algebraically and graphically. Students will investigate the concept of a polynomial and apply the remainder and factor theorems to solve problems. Students will learn to apply an understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation.
Identify Polynomials 2 concepts
Use the notation P(x) for polynomials and P(c) to indicate the value of P(x) for x=c
Identify a polynomial expression and describe the key features using appropriate terminology
Simplify Linear Expressions uing Polynomials 3 concepts
Division of polynomials
Add and subtract polynomials and multiply polynomials by linear expressions
State the degree of a polynomial after adding, subtracting, multiplying or dividing of one or more polynomials
Remainder and Factor Theorem 2 concepts
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 2 concepts
Sketch polynomials with degree no more than four by using the leading term, the roots and the x- and y-intercepts
Determine the effect of single, double and triple roots of a polynomial equation on the shape of the graph
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