&
Polynomials
Partial Fractions
Secondary A.Maths
Polynomials
What you'll learn:​
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Four Operations on Polynomials (Add, Subtract, Multiply & Divide)
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Use Remainder Theorem and Factor Theorem
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Factorise or determine factors of Cubic Expression
Polynomials
Four Operations on
Addition and Subtraction of Polynomials​
You can add or subtract polynomials by combining like terms.
Multiplication of Polynomials​
You can multiply two polynomials by using the "rainbow" method.
Division of Polynomials​
You can divide the polynomials by using the long division method as shown below.
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The working of a long division is no difference from our primary school method. Just that we are dividing it with the presence of algebra.
Watch the explanatory video to get tips and have a better understanding on how to do a long division.
Theorem
The
Remainder
There are two ways to obtain a remainder.
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Divide the polynomial using long division by a linear divisor ax - b.
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Substitute a solution into the polynomial.
​Both methods give the same answer.
However, you are required to know both the methods depending on nature of the questions asked.
Theorem
The
Factor
Factor Theorem is when a polynomial F(x) is EXACTLY DIVISIBLE by a linear divisor which gives a remainder of 0.
It is often used to factorise cubic polynomials which will be discussed in the following section.
Polynomials
Cubic
A cubic polynomial in x is a polynomial of degree 3 or x with a maximum power of 3.
For the cubic polynomial F(x),
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if the graph of y = F(x) cuts the x-axis at x = a, then x - a is a linear factor of F(x),
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the number of distinct real roots of the equation F(x) = 0 is the number of points of intersection of F(x) with the x-axis.
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the graph intersects the x-axis at up to 3 points. Hence it can have a maximum of 3 real roots.
Partial Fractions
What you'll learn:​
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Identify whether an algebraic fraction is a proper or an improper fractions
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Express proper algebraic fraction in its partial fractions
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Identify the various types of partial fractions
Proper & Improper
Fractions
Identifying
Given polynomials F(x) and G(x), where G(x) ≠ 0, written as a fraction is called algebraic fraction.
If the degree of the numerator F(x) is less than the degree of the denominator G(x), then it is a proper fraction.
Partial
Fractions
Identifying Types of
To express the proper fraction in partial fractions, factorise the denominator ​completely and write down the forms of the partial fractions as follows:
Watch the explanatory video to have a better understanding on how to identify the various types of partial fractions and get tips on how to express them in a much simpler ways.
Partial
Fractions
Expressing
Following are the example videos on how you can express the various types of partial fractions.
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Partial
Fractions
Advanced
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