Suppose p(x) is a polynomial with i...
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Suppose p(x) is a polynomial with integer coefficients. The remainder when p(x) is divided by X - 1 is 1 and the remainder when p(x) is divided by X-4 is 10. If r(x) is the remainder when px) is divided by (x - 1)(x - 4), find the value of r(2006).

JEE/Engineering Exams
Maths
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( p(x)=(x-1)(x-4)+a x+b ) ( p(1)=1 ) ( P(4)=10 ) ( a+b=1 ) ( 4 a+b=10 ) ( therefore quad 3 a=9 Rightarrow a=3 ) ( b=-2 ) ( p(x)=(x-1)(x-4)+3 x-2 ) ( r(x)=3 x-2 ) ( r(2006)=6018-2=frac{6016}{9} )
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