Question

If the polynomial p(x)=x4-2x³+3x²-ax+8 is divided by (x-2), it leaves a reminder 10. find the value of 'a'.​

Answer 1

Answer:

14

Explanation:

The remainder when  p  is divided by  x−1  is is  6 , therefore (remainder theorem)

p(1)=6 .

The other condition, can be written

p(−1)=14 .

These equations are written in terms of  a  and  b  as

1−2+3−a+b=6  

1+2+3+a+b=14 .

or

−a+b=4  

a+b=8 ,

and hence

a=2  

b=6 .

The remainder when  p  is divided by  x−2  is (remainder theorem again)

p(2)=16−16+12−4+6=14 .

Therefore, the remainder is 14.