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Question

If the remainder, when polynomial f(x) is divided by x1,x+1, are 6,8 respectively, then the remainder, when f(x) is divided by(x1)(x+1) is :

A
7x
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B
7+x
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C
8x
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D
8+x
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Solution

The correct option is A 7x
Since the divisor is quadratic, the remainder in general is assumed to be linear.
Thus remainder =ax+b.
f(x)= Quotient ×(x1)(x+1)+ Remainder

But by remainder theorem,
f(1)=6 and f(1)=8

a+b=6 and a+b=8
Solving simultaneously, we have
a=1 and b=7

The remainder is 7x

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