1. **State the problem:** Show that $(x + 4)$ is a factor of the polynomial $5x^3 - 73x + 28$. 2. **Recall the Factor Theorem:** A polynomial $f(x)$ has a factor $(x - a)$ if and only if $f(a) = 0$. Here, since the factor is $(x + 4)$, we check $f(-4)$. 3. **Evaluate the polynomial at $x = -4$:** $$f(-4) = 5(-4)^3 - 73(-4) + 28 = 5(-64) + 292 + 28 = -320 + 292 + 28$$ 4. **Simplify the expression:** $$-320 + 292 + 28 = (-320 + 292) + 28 = -28 + 28 = 0$$ 5. **Conclusion:** Since $f(-4) = 0$, by the Factor Theorem, $(x + 4)$ is indeed a factor of $5x^3 - 73x + 28$. 6. **Optional verification by polynomial division:** Dividing $5x^3 - 73x + 28$ by $(x + 4)$ will yield a polynomial quotient with no remainder, confirming the factor. **Final answer:** $(x + 4)$ is a factor of $5x^3 - 73x + 28$ because $f(-4) = 0$.