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Question

What must be subtracted from x36x215x+80 so that the result is exactly divisible by x2+x12?

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Solution


Let ax + b be subtracted from p(x)=x36x215x+80
so that it is exactly divisible by x2+x12.
s(x)=x36x215x+80(ax+b)
=x36x2(15+a)x+(80b)
Dividend = Divisor × quotient + remainder
But remainder will be zero.
Dividend = Divisor × quotient
s(x)=(x2+x12)×quotient
s(x)=x36x2(15+a)x+(80b)
Hence, x(4a)+(4b)=0,x0
4a=0 & (4b)=0
a=4 and b=4
Hence, if in p(x) we subtract 4x - 4 then it is exactly divisible by x2+x12
294778_312674_ans_cc5adb8e9863424abd08b9137ed9dd8c.png

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