(i) if both x-2 and x-1/2 are factors of px2 +5x + r , show that p=r

(ii)if the polynomial az3+4z2+3z-4 and z3-4z+a leave the same remainder when divided by z-3 find 'a'

(1)  Given polynomial is  –

Solving  (1)  and  (2)  –

Multiplying  (2)  by  4,  we obtained  –

Subtracting  (3)  from  (1),  we get  –

and so from  (1) ,  we get  –

Hence,  r  = p  =  –2

(2)  Given polynomials  are  –

Divide  p1(x)  by  z – 3  and get the remainder as follows :

Thus,  the remainder  is  –

Now divide  p2(x)  by  z 3  and get the remainder as given  below –

 

Here,  the remainder  is –

According to question  –

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