Question

s. The polynomial, f(x) = x4 – 2x2 + 3x2 - ax + b when divided by (x - 1) and (x + 1) leaves the
remainders 5 and 19 respectively. Find the values of a and b. Hence, find the remainder
when f(x) is divided by (x - 2).​

Answer 1

QUESTION - - -

The polynomial, f(x) = x4 – 2x2 + 3x2 - ax + b when divided by (x - 1) and (x + 1) leaves theremainders 5 and 19 respectively. Find the values of a and b.

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.

(MAY ATTACHMENT HELPS YOU)

Answer 2

Answer:

there is your answer in the attachment

if it helps mark it brainliast and follow