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

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Jim4109
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
x-6=0,x=6
put x=6 in the given eq. [tex]3 x^{3} -16 x^{2} -72=3( 6^{3} )-16( 6^{2} )-72 =3(216)-16(36)-72 [/tex]
=648-576-72
=648-648
=0
hence x-6 is a factor of the given polynomial