Question

( 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} )

# 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).

Solution