Question

factor the equation 12x4 - 27x3 6x2

Answer 1

Hello,

This is not an equation but an expression.
We must see the sign "=" in a equation!

Netherless,

12x^4-27x^3+6x²=3x²(4x²-9x+2)=3x²(4x²-8x-x+2)
=3x²(4x(x-2)-1(x-2))
=3x²(x-2)(4x-1)

Answer 2

assuming that that is a plus between 12x^3 and 6x^2
factor each
12x^4=2*2*3*x*x*x*x
27x^3=3*3*3*x*x*x
6x^2=2*3*x*x

GCF=3*x*x=3x^2
undistribute
(3x^2)(4x^2-9x+2)
factor 4x^2-9x+2
trial and error
(4x-1)(x-2)
(3x^2)(4x-1)(x-2)