Factor 5x^3-45x

Problem

5*x3−45*x

Solution

1. Identify the greatest common factor (GCF) of the terms 5*x3 and 45*x

2. Factor out the GCF, which is 5*x from the expression.

5*x*(x2−9)

3. Recognize the pattern in the remaining binomial x2−9 as a difference of squares, which follows the form a2−b2=(a−b)*(a+b)

4. Factor the difference of squares by identifying a=x and b=3

5*x*(x−3)*(x+3)

Final Answer

5*x3−45*x=5*x*(x−3)*(x+3)

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