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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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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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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Expand and simplify .
A cuboid has a length of units, a width of units, and a height of units. 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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