Polynomials (OCR A Level Maths: Pure)

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 .

Given that , where  are constants, find the values of .

Factorise completely .

Divide  by .

Find the remainder when is divided by .

Given that  is a factor of , factorise completely.

Show that  where  are constants to be found.

Hence factorise completely.

Write down all the real roots of the equation .

Use the factor theorem to show that is a factor of .

Factorise  completely.

Write down all the real roots of the equation .

. Given that and :

find the values of  and .

Factorise  completely.

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 .

Given that , where  are constants, find the values of  and .

Factorise completely .

Divide  by .

Find the remainder when is divided by .

Given that  is a factor of , factorise  completely.

Show that where  and  are constants to be found.

Hence factorise  completely.

Write down all the real roots of the equation .

Use the factor theorem to show that  is a factor of .

Factorise  completely.

Write down all the real roots of the equation .

. Given that  and : 

find the values of  and .

Factorise  completely.

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 .

Given that , where  and are constants, find the values of  and .

Factorise completely .

Divide  by .

Find the remainder when  is divided by .

Given that  is a factor of , factorise  completely.

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.

Given that 3 is a root of the equation , prove that the equation has no other real roots.

Show that  and .

Hence, solve .