Use the Factor Theorem to determine whether g(x) is factor of f(x) or not.
f(x)=3x3+x2−20x+12,g(x)=3x−2
Given f(x)=3x3+x2−20x+12 the g(x)=3x−2 is the factor
If g(x)=3x−2 is factor then g(x)=3x−2=0 or x=23
Replace x by 23 in f(x) we get
f(x)=3x3+x2−20x+12
f(23)=3(23)3+(23)2−20(23)+12
⇒f(23)=3×827+49−20×23+12
f(23)=89+49−403+12
f(23)=8+4−120+1089=120−1209=0
So f(x)is zero by g(x) then g(x) =3x-2 is factor of f(x)=3x3+x2−20x+12