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Question

# The polynomial f(x)=x4âˆ’2x3+3x2âˆ’ax+b when divided by (xâˆ’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 (xâˆ’2)

A
a=6,b=8 and remainder=10
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B
a=5,b=8 and remainder=10
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C
a=5,b=7 and remainder=10
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D
None of these
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Solution

## The correct option is B a=5,b=8 and remainder=10 by remainder theorem, f(1)=5 and f(−1)=19 ∴1−2+3−a+b=5⇒b−a=3 and 1+2+3+a+b=19⇒a+b=13 b=8 a=5 and remainder when f(x) is divided by (x−2) is f(2)=16−16+12−10+8=10

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