2.1 Polynomials

Given that  is a factor of , factorise  completely.

. Given that   and  :

 find the values of  and .

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.

Show that can be written in the form  where  and  are constants to be found.

Find the remainder when is divided by .

Given that  is a factor of , factorise  completely.

Factorise  completely.

Write down all the real roots of the equation .

. Given that and  :

find the values of  and  .

Factorise completely.

Consider the function 

Find the quotient and remainder when is divided by  

Hence write   in the form where  and  are constants to be determined.

The function   has  as a factor, and when  is divided by the remainder is 7. 

Show that and  must satisfy the simultaneous equations:  
         

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