Factor 2x^3-18x

Problem

2*x^3−18*x

Solution

1. Identify the greatest common factor by looking at the coefficients and the variables in both terms.

2. Factor out the greatest common factor, which is 2*x from the expression.

2*x*(x^2−9)

3. Recognize the difference of squares inside the parentheses, as x^2 and 9 are both perfect squares (x^2 and 3^2.

4. Apply the difference of squares formula, a^2−b^2=(a−b)*(a+b) to factor the remaining quadratic expression.

2*x*(x−3)*(x+3)

Final Answer

2*x^3−18*x=2*x*(x−3)*(x+3)

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