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

When f(x) is divided by x−1 and x+1, the remainders are 5 and 19 respectively.

Therefore, f(1)=5 and f(−1)=19

1−2+3−a+b=5 and 1+2+3+a+b=19

−a+b=3 and a+b=13

Adding these two, we get,

b=8

Therefore, a=5

Substituting these values of a and b in f(x), we get,

f(x)=x 4−2x 3 +3x 2−5x+8

The remainder when f(x) is divided by x−2 is equal to f(2).

Therefore,

Remainder = f(2)=2 4 −2×2 3+3×2 2−5×2+8=10

Answer 2

Answer:

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Question:

f 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:

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