Question 193258
P(x)=3x^3+7x^2-2x-6
(x-3)
3|,  3,,7,,-2,,,,6
,,,,,,,,,,9,,,48,,138
_________________
,,,,,3,,16,,46,,144,,,,,REM  144

P(3)=  3*3^3+7*3^2-2*3+6
p(3)=81 +63-6+6=144
(x+2)
-2|,,,,3,,,,7,,,,-2,,,,6
,,,,,,,,,,,,,,,-6,,,-2,,,8 
____________________
,,,,,,,,,3,,,,,1,,,,-4,,,14   ,,,,,rem14

P(-2)=  3(-2)^3+7(-2)^2-2(-2)+6
P(-2)=-24+28+4+6=14

(x+1)
-1|,,,,,3,,,,7,,,,,-2,,,,6
,,,,,,,,,,,,,,,-3,,,,-4,,,,6
____________________
,,,,,,,,,,3,,,,4,,,,,-6,,,12,,,,,REM12
P(-1)=  3(-1)^3+7(-1)^2-2(-1)+6
P(-1)+ -3=7=2=6=12
(x-5)
5|,,,,3,,,,,7,,,,,-2,,,,6
,,,,,,,,,,,,,15,,,110,,,540
_______________________
,,,,,,,3,,,,22,,,,108,,546,,,,,,REM  546
P(5)=  3(5)^3=7(5)^2-2(5)+6
P(5)=375+175-10+6=546

instructor  probably  just  wanted  you  to  recognize  remainder  theorem,  and  calc  P(x)

please  excuse  all  the  commas,  just  trying  to allign  numbers