Question

The polynomials p(x) = ax^3 + 4x^2 + 3x - 4 and q(x) = x^3 - 4x =a leave tge same remainder when divided by x-3. find the remainder when p(x) is divided by (x-2)

Answer 1

x-3=0
x=3
p(x)=ax^3+4x^2+3x-4
p(3)=a(3)^3+4(3)^2+3(3)-4
=27a+36+9-4
=27a+36+5
=27a+41
27a= -41
q(x)=x^3-4x=a
q(3)=(3)^3-4(3)-a=0
=27-12-a
=15-a
a=15
x-2=0
x=2
p(2)=15(2)^3+4(2)^2+3(2)-4
=120+16+6-4
=136+2
=138