Question

examine whether x+2 is a factore of x^3+3x^2+5x+6 and of 2x+4

Answer 1

solution - the zero of x+2 is -2
now. let p(x)=x^3+3x^2+5x+6 and z(x)=2x+4
then we get p(-2)=(-2)^3+3(-2)^2+5(-2)+6
=-8+12-10+6
=0
so by using factor theorem , x+2 is a factor of x^3+3x^2+5x+6
now we will find z(-2)=2(-2)+4=0
so we finally conclude that x+2 is a factor of both p(x) and z(x)..
hope it helps..◆●◆