Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 4 - Polynomials - 4.3 Polynomials - 4.3 Exercise Set: 35

Answer

The answers are: The standard form of this polynomial is written as $\color{red}{8t^4 + t^3 + 5t}$. \begin{align} &\text{a) The degree of the terms are: }\color{red}{4, 3, 1} \\ &\text{b) The leading term and coefficient is: }\color{red}{8t^4} \\ &\text{c) The degree of the polynomial is: }\color{red}4 \end{align}

Work Step by Step

To identify the degree and the leading coefficient of the polynomial, we first write it in the standard form and look at the first term. The standard form is when the terms' exponents are arranged in descending order from left to right. The exponent of the first term is the degree of the polynomial and the coefficient of the first term is the leading coefficient. The standard form of this polynomial is written as $\color{red}{8t^4 + t^3 + 5t}$. \begin{align} &\text{a) The degree of the terms are: }\color{red}{4, 3, 1} \\ &\text{b) The leading term and coefficient is: }\color{red}{8t^4} \\ &\text{c) The degree of the polynomial is: }\color{red}4 \end{align}
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