Solving a Cubic Equation by Factoring

Published on October 18, 2026

Algebra

This problem involves solving the cubic equation 2x^3 + 2x^2 - 24x = 0 by factoring out the greatest common factor and then factoring the resulting quadratic expression.

Question

Answer

Step 1 — Factor out the GCF :

Step 2 — Factor the quadratic

using two numbers that multiply to

and add to

(namely

and

Step 3 — Apply the Zero Product Property, setting each factor to zero:

Final answer:

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