Question

Identify the degree, leading term, and leading coefficient of the following polynomial functions.

Answer 1

Explanation:

First, we define the required terms below:

• The degree of a function is the highest power in the function.

,

• The leading term is the term that contains the degree.

,

• The leading coefficient is the coefficient of the variable in the leading term.

Part A

Given the function:

`\begin{gathered} \begin{equation*} f(c)=2c^4-8c^1-6c^5 \end{equation*} \\ Degree:5 \\ Leading\text{ term:}-6c^5 \\ \text{ Leading Coefficient: }-6 \end{gathered}`

Part B

Given the function:

`\begin{equation*} g(p)=17p^4+17p^6+11p^2 \end{equation*}`

Arrange in descending power of p.

`\begin{gathered} g(p)=17p^6+17p^4+11p^2 \\ \implies Degree:6 \\ Leading\text{ Term: }17p^6 \\ \text{ Leading coefficient: }17 \end{gathered}`

Part C

Given the function:

`\begin{equation*} h(p)=-7p^(11)+7p^(21)-18p^(17) \end{equation*}`

Arrange in descending power of p.

`\begin{gathered} h(p)=7p^(21)-18p^(17)-7p^(11) \\ Degree=21 \\ Leading\;Term=7p^(21) \\ Leading\;Coefficient=7 \end{gathered}`