Question

Examine whether x+2 is a factor of x3+3x2+5x+6 and of 2x+4.

Answer 1

It can be easily checked by putting - 2 in both equations and looking whether the answer is zero or not
x3+3x2+5x+6=(-2)^3+3(-2)^2+5(-2)+6=0
2x+4=2(-2)+4=0
Thus x+2 is factor of both given functions

Answer 2

p(x)=x^3+3x^2+5x+6

g(x)=x+2

       x=-2

put x=-2 in p(x)

p(-2)=(-2)^3+3(-2)^2+5(-2)+6

       =-8+12-10+6

      =0

since p(x) is zero 

x+2 is a factor of x3+3x2+5x+6

checking:::::-

let x=-2

q(x)=2x+4

q(-2)=2(-2)+4

       =-4+4

       =0

since reminder is zero

x+2 is a factor of 2x+4