Factored Polynomial 7Dbc90

1. **State the problem:** We need to write a polynomial in factored form given the roots $-6$, $-2$, and $-4$. 2. **Recall the Factor Theorem:** If $r$ is a root of a polynomial, then $(x - r)$ is a factor of that polynomial. 3. **Apply the Factor Theorem to each root:** - For root $-6$, factor is $(x - (-6)) = (x + 6)$ - For root $-2$, factor is $(x - (-2)) = (x + 2)$ - For root $-4$, factor is $(x - (-4)) = (x + 4)$ 4. **Write the polynomial in factored form:** $$ (x + 6)(x + 2)(x + 4) $$ 5. **Explanation:** Each factor corresponds to a root. Multiplying these factors will give a polynomial with exactly these roots. **Final answer:** $$ (x + 6)(x + 2)(x + 4) $$