Factoring Out the GCF Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Factor −18x4y2+12x3y3−6x2y-18x^4y^2 + 12x^3y^3 - 6x^2y.

Solution

  1. 1
    GCF: coefficients GCF = 6, min power of xx is x2x^2, min power of yy is yy. GCF = 6x2y6x^2y. Factor out −6x2y-6x^2y (negative to make leading term positive).
  2. 2
    −6x2y(3x2y−2xy2+1)-6x^2y(3x^2y - 2xy^2 + 1).

Answer

−6x2y(3x2y−2xy2+1)-6x^2y(3x^2y - 2xy^2 + 1)
With multiple variables, find the GCF for each variable separately. Factoring out a negative GCF when the leading term is negative keeps the remaining expression cleaner.

About Factoring Out the GCF

Factoring out the greatest common factor (GCF) means identifying the largest expression that divides every term, then rewriting the polynomial as that GCF times what remains.

Learn more about Factoring Out the GCF →

More Factoring Out the GCF Examples

Example 1 easy

Factor [formula].

Example 2 medium

Factor [formula].

Example 3 easy

Factor [formula].

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