\(12x^5y^3 - 8x^3y^2 + 4x^4y\)

Factor the expression.

12x^5 y^3 - 8x^3 y^2 + 4x^4 y

• common factor: 4 x^3 y
• inside: (12x^5 y^3)/(4x^3 y) = 3x^2 y^2 (-8x^3 y^2)/(4x^3 y) = -2y (4x^4 y)/(4x^3 y) = x

So the factorization is: 4 x^3 y (3 x^2 y^2 - 2 y + x)

Equivalently: 4 x^3 y (3 x^2 y^2 + x - 2 y)

This inner factor does not factor nicely over the integers, so this is the complete factorization.