Polynomial Ordering 674E1C

1. **State the problem:** We need to find the proper ordering of the polynomial $$14x^3 - 6x^7 + 20x^5 + 5x^2$$. 2. **Recall the rule for ordering polynomials:** Polynomials are typically ordered in descending powers of $$x$$, starting from the highest exponent to the lowest. 3. **Identify the powers of $$x$$ in each term:** - $$14x^3$$ has power 3 - $$-6x^7$$ has power 7 - $$20x^5$$ has power 5 - $$5x^2$$ has power 2 4. **Order the terms from highest to lowest power:** - Highest power is $$7$$, so $$-6x^7$$ comes first - Next is power $$5$$, so $$20x^5$$ comes second - Then power $$3$$, so $$14x^3$$ comes third - Finally power $$2$$, so $$5x^2$$ comes last 5. **Write the polynomial in proper order:** $$-6x^7 + 20x^5 + 14x^3 + 5x^2$$ 6. **Compare with the given options:** The correct ordering matches the option: - $$-6x^7 + 20x^5 + 14x^3 + 5x^2$$ **Final answer:** $$-6x^7 + 20x^5 + 14x^3 + 5x^2$$