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Question

The polynomial f(x)=x42x3+3x2ax+b when divided by (x1) 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 (x2)

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
12+3a+b=5ba=3 and
1+2+3+a+b=19a+b=13
b=8 a=5
and remainder when f(x) is divided by (x2) is
f(2)=1616+1210+8=10

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