Factor 3x^2+12x+12

Problem

3*x^2+12*x+12

Solution

1. Identify the greatest common factor (GCF) for all terms in the expression.

2. Factor out the GCF, which is 3 from the expression.

3*(x^2+4*x+4)

3. Recognize the quadratic expression inside the parentheses as a perfect square trinomial of the form a^2+2*a*b+b^2

4. Factor the trinomial x^2+4*x+4 into (x+2)^2

3*(x+2)*(x+2)

Final Answer

3*x^2+12*x+12=3*(x+2)^2

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