Simplify
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Simplify
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Factorise
Hence simplify
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Simplify fully
Simplify fully
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The function is given by .
Show that .
Hence, or otherwise, write down the real solutions to the equation
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The function is given by
Work out and hence write down a factor of .
Work out .
Write in the form where are integers to be found.
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Which one of the following algebraic fractions is improper? Explain your answer.
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Find the remainder when is divided by .
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Given that
where are integer constants.
In terms of and/or as appropriate
Find the values of .
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The function is given by
where are integer constants.
It is also given that .
Find the values of .
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Simplify
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Simplify fully
Simplify fully
Simplify fully
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The function is given by
Show that .
Hence write down a factor of .
Fully factorise .
Write down the solutions to the equation .
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Show that is a factor of .
Fully factorise .
Find all the real solutions to .
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Given that is a factor of find the value of .
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Work out .
Work out .
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Given
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One of the three algebraic fractions below is improper (‘top-heavy’).
Identify which fraction is improper and write it in the form , where and are integers to be found.
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Simplify fully
Hence solve the equation .
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It is given that
Find .
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The result of dividing by is .
Find the values of and .
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Simplify fully
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Simplify fully
Simplify fully
Simplify fully
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The function is given by
Show that is a factor of .
Hence, or otherwise, fully factorise .
Write down the roots of .
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Show that is a factor of .
Hence find all the real solutions to the equation .
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Given that is a factor of find the value of .
Hence, or otherwise, fully factorise .
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Work out .
Work out .
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Find the remainder when is divided by .
Find the value of when .
Comment on your answers to parts (i) and (ii).
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One of the three algebraic fractions below is improper (‘top-heavy’):
Identify which fraction is improper and write it in the form , where and are integers to be found.
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Simplify
Hence solve .
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It is given that
Why would assuming that be a logical first step in attempting to determine the precise forms of and ?
By first making the assumption from part (a), find .
Explain, with an example, why the forms of and determined in parts (a) and (b) are not the only possible forms for those functions.
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When is divided by the quotient is and the remainder is .
Find the values of and .
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Simplify fully
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Simplify fully
Simplify fully
Simplify fully
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Given that is a factor of the function
find the value of and fully factorise .
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Show that is a factor of and hence find all the real solutions to the equation .
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Show that is a factor of .
Given that is a root of , find the value of .
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Work out .
Work out
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For a polynomial , the Remainder Theorem states that
When is divided by the remainder is .
Use the Remainder Theorem to find the remainder when is divided by .
Work out the remainder when is divided by .
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One of the three algebraic fractions below is improper (‘top-heavy’):
Identify which fraction is improper and rewrite it as a quotient and a remainder term.
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Solve
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It is given that
where and are integers.
Find the values of .
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When is divided by the quotient is and the remainder is .
Find the values of and .
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