SMO Q10(senior category)
When a polynomial is divided by and , the remainders are -6 and 6 respectively. Let be the remainder when is divided by . Find the value of .
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1 solution
f(x)=(x-1)p - 6 So f(1)=(-6) f(x)=q(x+5)+6 So f(-5)=6 These are for some Integers p and q Now, f(x)=t(x-1)(x+5)+ r(x).....(3) As r(x) is the remainder its degree will be less than the divisor So r(x)= ax+b for a and b being Integers Now Putting this in (3) f(x)=t(x-1)(x+5)+ ax+b Putting f(1) we get a+b=-6 and putting f(-5) we get -5a+b=6 Upon solving we get a=-2 and b=-4 So r(x)=-2x-4 So r(-2)= 0