Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
Let's begin by defining the key terminologies:
The degree of a polynomial simply refers to the term with the highest exponent in a polynomial
For example:
[tex]\begin{gathered} a+8\Rightarrow a^1+8 \\ =a^1+8 \\ \text{We will observe that the variable ''a'' has a degree of ''1''} \\ \text{Therefore, the degree of this polynomial will be ''1''} \\ \\ \text{If we have}\colon5a^2+10 \\ 5a^2+10 \\ \text{We will observe that the variable ''a'' has the highest degree of ''2''} \\ \text{Therefore, the degree of this polynomial will be ''2''} \\ \\ \text{If we have}\colon3a^4+2a^2+10a+10 \\ 3a^4+2a^2+10a+10 \\ \text{We will observe that the variable ''a'' has the highest degree of ''4'' } \\ \text{Therefore, the degree of this polynomial will be ''4''} \end{gathered}[/tex]The leading coefficient simply refers to the coefficient of the term that has the highest degree in a polynomial
For example:
[tex]\begin{gathered} \text{If we have}\colon a+8 \\ a+8 \\ \text{''a'' is the variable having the highest degree, that degree is ''1''} \\ \text{The coefficient of the variable ''a'' is 1. Hence, the leading coefficient is ''1''} \\ \\ \text{If we have}\colon5a^2+10 \\ 5a^2+10 \\ \text{''}5a^2\text{'' is the variable with the highest degree},\text{ that is ''2''} \\ \text{The coefficient of the variable ''}5a^2\text{'' is 5. Hence, the leading coefficient is ''5''} \\ \\ \text{If we have}\colon3a^4+2a^2+10a+10 \\ 3a^4+2a^2+10a+10 \\ \text{ ''}3a^4\text{'' is the variable with the highest degree},\text{ that is ''4''} \\ \text{The coefficient of the variable ''}3a^4\text{'' is ''3''. Hence, the leading coefficient is ''3''} \end{gathered}[/tex]
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.