Expand and simplify
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Expand and simplify
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Use the factor theorem to verify that is a factor of .
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Factorise
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Divide by .
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Given has a root at , fully factorise .
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Use polynomial division to show that is a factor of .
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Given is a root of the function , fully factorise .
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Given that is a factor of , find the value of .
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Given that is a root of the function , find the possible values of .
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Given that is a factor of , fully factorise .
Sketch the graph of , labelling the coordinates of all points where the graph intersects the coordinate axes.
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Find the remainder when is divided by .
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The function is given by , where and are constants.
Given that both and are factors of find the values of and .
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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 and are integers to be found.
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Find the remainder when is divided by
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Given that
where and are integer constants.
In terms of and/or as appropriate
Find the values of and .
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The function is given by
where and are integer constants.
It is also given that
Find the values of and .
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Expand and simplify .
A rectangle has side lengths of units and units. Find an expression for the area of the rectangle in terms of and .
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Given that , where are constants, find the values of .
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Factorise completely .
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Divide by .
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Find the remainder when is divided by .
Given that is a factor of , factorise completely.
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Show that where are constants to be found.
Hence factorise completely.
Write down all the real roots of the equation .
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Use the factor theorem to show that is a factor of .
Factorise completely.
Write down all the real roots of the equation .
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. Given that and :
find the values of and .
Factorise completely.
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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 thatis 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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Given
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It is given that
Find .
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The result of dividing
Find the values of and .
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Consider the function
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The function has as a factor, and when is divided by the remainder is 7.
Show that and must satisfy the simultaneous equations:
Hence find and
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Expand and simplify .
A square has side lengths of units. Find an expression for the length of the diagonal of the square in terms of and .
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Given that , where are constants, find the values of and .
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Factorise completely .
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Divide by .
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Find the remainder when is divided by .
Given that is a factor of , factorise completely.
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Show that where and are constants to be found.
Hence factorise completely.
Write down all the real roots of the equation .
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Use the factor theorem to show that is a factor of .
Factorise completely.
Write down all the real roots of the equation .
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. Given that and :
find the values of and .
Factorise completely.
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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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[2]
[1]
[1]
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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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Given that is a factor of the function and that the remainder when is divided by is , find the values of the constants p and q.
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Show that can be written in the form where and are constants to be found.
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Expand and simplify .
A cuboid has a length of units, a width of units, and a height of . Find an expression for the volume of the cuboid in terms of and .
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Given that , where and are constants, find the values of and .
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Factorise completely .
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Divide by .
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Find the remainder when is divided by .
Given that is a factor of , factorise completely.
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Show that where and are constants to be found.
Given that is a factor of , factorise completely.
Hence show that the equation has exactly 2 real roots.
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Given that 3 is a root of the equation , prove that the equation has no other real roots.
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Show that and .
Hence, solve .
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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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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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When is divided by the quotient is and the remainder is .
Find the values of and .
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