How do you factor 3x^3-4x^2-28x-16 given that x – 4 is a factor?

Answer 1

3x^3-4*3x^2+12x^2-4x^2-28x-16

=3x^2(x-4)+8x^2-4*8x+32x-28x-16

=3x^2(x-4)+8x(x-4)+4x-16

=(x-4)(3x^2+8x-16)

=(x-4)(3x^2+12x-4x-16)

=(x-4)(3x(x+4)-4(x+4))

=(x-4)(x+4)(3x-4)