Question

If f( x)=x^ 4 -2x^ 3 +3x^ 2 -9x+1 b is a polynomial such that when it is divided by x - 1 and x + 1 . the remainders are respectively 5 and 19. Determine the remainder when I(x, ) is divided by (x-2)​

Answer 1

ANSWER - - -

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.

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