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\begin{tabular}{l} Find the degree of the polynomial. \\ SUBMIT ANSWER \\ SU \( s^{4}-3 r^{4} s^{5} \) \\ \hline\end{tabular}

Ask by Dawson Ayala. in the United States
Jan 24,2025

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Tutor-Verified Answer

Answer

The degree of the polynomial \( s^{4}-3r^{4}s^{5} \) is 5.

Solution

Calculate or simplify the expression \( s^{4}-3r^{4}s^{5} \). Simplify the expression by following steps: - step0: Solution: \(s^{4}-3r^{4}s^{5}\) The degree of the polynomial \(s^{4}-3r^{4}s^{5}\) is 5.

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Extra Insights

The degree of a polynomial is determined by the highest power of the variable in the expression. In the polynomial \( s^{4} - 3 r^{4} s^{5} \), we have two terms: \( s^{4} \) and \( -3 r^{4} s^{5} \). The highest power of \( s \) is 5, which appears in the second term. Therefore, the degree of the polynomial is 5. Additionally, remember that if a polynomial has more than one variable, you should focus on the degrees of each term. The overall degree of the entire polynomial is defined by the highest sum of the exponents in all the variables in a term. In this case, the term \( -3 r^{4} s^{5} \) has a total degree of \( 4 + 5 = 9 \) when considering both variables \( r \) and \( s \).

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