- Mathematics Advanced
- Year 10
Polynomials
approx. 8 hrs
7 topics
22 concepts
Gain proficiency when working with polynomials.
approx. 8 hrs
7 topics
22 concepts
Gain proficiency when working with polynomials.
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.
This learning program is made up of the following 7 topics, broken down into 22 concepts.
Log of a product
Log of a quotient
Log of a power
Log of a reciprocal
Log of a base
Log of 1
Simplify expressions using the laws of logarithms
Solving exponential equations by taking the logarithm of both sides.
Solving exponential equations by equating the power
Converting logarithmic form to exponential form
Converting exponential form to logarithmic form
Solve simple equations that involve logarithms
Draw and compare the graphs of the inverse functions y=a^x and y=logax
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 the x- and 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
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
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