Factor 5x^3+40

Problem

5*x^3+40

Solution

1. Factor out the greatest common factor, which is 5

5*(x^3+8)

2. Identify the expression inside the parentheses as a sum of two cubes, since 8=2^3

5*(x^3+2^3)

3. Apply the formula for the sum of cubes, a^3+b^3=(a+b)*(a^2−a*b+b^2) where a=x and b=2

5*(x+2)*(x^2−(x)*(2)+2^2)

4. Simplify the terms inside the quadratic factor.

5*(x+2)*(x^2−2*x+4)

Final Answer

5*x^3+40=5*(x+2)*(x^2−2*x+4)

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