Factoring Out the GCF Math Example 2

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Example 2

medium
Factor 12x3−8x2+4x12x^3 - 8x^2 + 4x.

Solution

  1. 1
    Step 1: GCF of 12, 8, 4 is 4. Minimum power of xx is x1x^1. GCF = 4x4x.
  2. 2
    Step 2: 12x3÷4x=3x212x^3 \div 4x = 3x^2, 8x2÷4x=2x8x^2 \div 4x = 2x, 4x÷4x=14x \div 4x = 1.
  3. 3
    Step 3: 4x(3x2−2x+1)4x(3x^2 - 2x + 1).
  4. 4
    Check: Redistribute to verify 4x⋅3x2=12x34x \cdot 3x^2 = 12x^3, 4x⋅(−2x)=−8x24x \cdot (-2x) = -8x^2, 4x⋅1=4x4x \cdot 1 = 4x ✓

Answer

4x(3x2−2x+1)4x(3x^2 - 2x + 1)
With three terms, find the GCF of all coefficients and the lowest power of xx present. The GCF is always the first step in any factoring problem.

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.

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More Factoring Out the GCF Examples

Example 1 easy

Factor [formula].

Example 3 easy

Factor [formula].

Example 4 hard

Factor [formula].

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