Factor 3x^2-18x+27

Problem

3*x^2−18*x+27

Solution

1. Identify the greatest common factor (GCF) of all three terms, which is 3

2. Factor out the GCF from the expression to simplify the quadratic.

3*(x^2−6*x+9)

3. Recognize the pattern inside the parentheses as a perfect square trinomial of the form a^2−2*a*b+b^2=(a−b)^2

4. Identify the terms where a=x and b=3 since x^2 is the square of x 9 is the square of 3 and $2(x)(3) = 6x$.

5. Rewrite the expression in its factored form.

3*(x−3)^2

Final Answer

3*x^2−18*x+27=3*(x−3)^2

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