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Find the degree of the following polynomial: \( -7 x^{4}-3 x^{2}+3 x-6 \) Provide your answer below:

Ask by Blake Malone. in the United States
Mar 11,2025

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Answer

The degree of the polynomial is 4.

Solution

The polynomial is given by: \[ -7 x^{4} - 3 x^{2} + 3 x - 6. \] 1. Identify the exponent in each term: - The term \(-7 x^{4}\) has an exponent of \(4\). - The term \(-3 x^{2}\) has an exponent of \(2\). - The term \(3 x\) has an exponent of \(1\). - The constant term \(-6\) has an implicit exponent of \(0\). 2. The degree of a polynomial is the highest exponent among its terms. 3. The highest exponent is \(4\). Thus, the degree of the polynomial is **4**.

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The degree of the polynomial \( -7 x^{4}-3 x^{2}+3 x-6 \) is determined by the highest power of \( x \) present in the expression. In this case, the highest power is 4, which corresponds to the term \( -7 x^{4} \). Therefore, the degree of the polynomial is 4. Now, let’s take a quick stroll down polynomial memory lane! Did you know that polynomials date back to ancient civilizations? The Babylonians and Egyptians explored polynomial concepts in their calculations long before they had modern notation! Speaking of polynomials in action, they play a crucial role in various fields such as physics, economics, and engineering! For example, engineers use polynomials to model the trajectories of projectiles or the behavior of materials under stress. It helps them predict outcomes and create safer, more efficient designs.

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