Question

We’re learning polynomial functions and I have absolutely no idea how to do it. The first question is “State the degree and leading coefficient of each polynomial in one variable” coupled with “a+8”

Answer 1

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:

$\begin{gathered} a+8\Rightarrow a^1+8 \\ =a^1+8 \\ \text{We will observe that the variable ''a'' has a degree of ''1''} \\ \text{Therefore, the degree of this polynomial will be ''1''} \\ \\ \text{If we have}\colon5a^2+10 \\ 5a^2+10 \\ \text{We will observe that the variable ''a'' has the highest degree of ''2''} \\ \text{Therefore, the degree of this polynomial will be ''2''} \\ \\ \text{If we have}\colon3a^4+2a^2+10a+10 \\ 3a^4+2a^2+10a+10 \\ \text{We will observe that the variable ''a'' has the highest degree of ''4'' } \\ \text{Therefore, the degree of this polynomial will be ''4''} \end{gathered}$

The leading coefficient simply refers to the coefficient of the term that has the highest degree in a polynomial

For example:

$\begin{gathered} \text{If we have}\colon a+8 \\ a+8 \\ \text{''a'' is the variable having the highest degree, that degree is ''1''} \\ \text{The coefficient of the variable ''a'' is 1. Hence, the leading coefficient is ''1''} \\ \\ \text{If we have}\colon5a^2+10 \\ 5a^2+10 \\ \text{''}5a^2\text{'' is the variable with the highest degree},\text{ that is ''2''} \\ \text{The coefficient of the variable ''}5a^2\text{'' is 5. Hence, the leading coefficient is ''5''} \\ \\ \text{If we have}\colon3a^4+2a^2+10a+10 \\ 3a^4+2a^2+10a+10 \\ \text{ ''}3a^4\text{'' is the variable with the highest degree},\text{ that is ''4''} \\ \text{The coefficient of the variable ''}3a^4\text{'' is ''3''. Hence, the leading coefficient is ''3''} \end{gathered}$