Question

briefly explain the process by which you would determine whether or not x-6 a factor of 3x^3-16x^2-72

Answer 1

x-6=0,x=6
put x=6 in the given eq.
`3 x^(3) -16 x^(2) -72=3( 6^(3) )-16( 6^(2) )-72 =3(216)-16(36)-72`
=648-576-72
=648-648
=0
hence x-6 is a factor of the given polynomial

Answer 2

Using the remainder theorem, substitute 6 in for any x in the equation and it will equal the remainder if it has been divided by (x-6). If the remainder is zero, then it would have divided evenly...making it a factor. If it equals anything but zero then it would not be a factor