1. Stating the problem: Factor and simplify the cubic polynomial $$4x^3 + 16x^2 + 12x$$. 2. First, look for the greatest common factor (GCF) among all the terms. - The coefficients are 4, 16, and 12. The GCF of 4, 16, and 12 is 4. - All terms contain at least one factor of $$x$$. So, the GCF is $$4x$$. 3. Factor out the GCF $$4x$$ from the polynomial: $$4x^3 + 16x^2 + 12x = 4x(x^2 + 4x + 3)$$. 4. Next, factor the quadratic inside the parentheses, $$x^2 + 4x + 3$$. - Look for two numbers that multiply to 3 and add to 4. - These numbers are 3 and 1. So, $$x^2 + 4x + 3 = (x + 3)(x + 1)$$. 5. Write the fully factored form: $$4x(x + 3)(x + 1)$$. 6. Final answer: The factorization of $$4x^3 + 16x^2 + 12x$$ is $$4x(x + 3)(x + 1)$$.