Polynomial Ordering 023Fc4

1. **State the problem:** We need to find the proper ordering of the polynomial $2x^3 + 4x^5 + 16x - 7$. 2. **Recall the rule for ordering polynomials:** Polynomials are typically ordered by descending powers of $x$, starting from the highest degree term to the lowest. 3. **Identify the degrees of each term:** - $4x^5$ has degree 5 - $2x^3$ has degree 3 - $16x$ has degree 1 - $-7$ is a constant term with degree 0 4. **Order the terms from highest to lowest degree:** $$4x^5 - 2x^3 + 16x - 7$$ 5. **Check the options:** - $16x + 4x^5 - 2x^3 - 7$ (incorrect, starts with degree 1 term) - $16x - 7 + 4x^5 - 2x^3$ (incorrect, terms not in descending order) - $-7 + 16x - 2x^3 + 4x^5$ (incorrect, ascending order) - $4x^5 - 2x^3 + 16x - 7$ (correct, descending order) **Final answer:** $4x^5 - 2x^3 + 16x - 7$