Polynomials (OCR A Level Maths: Pure)

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

Factorise

 

  

Divide  by  .

Given  has a root at , fully factorise .

Use polynomial division to show that  is a factor of .

Given  is a root of the function , fully factorise .

Given that  is a factor of , find the value of .

Given that  is a root of the function , find the possible values of .

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.

Find the remainder when  is divided by .

The function  is given by , where  and  are constants.

Given that both and  are factors of  find the values of and .