QuestionAnswer the questions about the following polynomial.
Answer Attempt 1 out of 2
The expression represents a polynomial with terms. The constant term is , the leading term is , and the leading coefficient is .
Studdy Solution
STEP 1
What is this asking?
We're looking at a polynomial and figuring out its degree, how many terms it has, its constant term, its leading term, and its leading coefficient.
Watch out!
Don't mix up the constant term and the leading coefficient!
Also, remember to write the polynomial in standard form before identifying the leading term and leading coefficient.
STEP 2
1. Rewrite in standard form
2. Identify the degree
3. Count the terms
4. Find the constant term
5. Find the leading term and leading coefficient
STEP 3
Let's **rewrite** our polynomial in standard form, which means ordering the terms from highest degree to lowest degree.
This will help us clearly see the leading term and the degree of the polynomial.
Our polynomial is .
Rewriting it in standard form, we get .
STEP 4
The **degree** of a polynomial is the highest power of that appears.
Looking at our standard form polynomial , we see the highest power is **4**.
So, the degree of our polynomial is **4**.
It's a **quartic** polynomial!
STEP 5
A **term** is a single number or variable, or numbers and variables multiplied together.
Let's count them in our polynomial .
We have , , , and .
That's **four** terms!
STEP 6
The **constant term** is the term without any variables.
In our polynomial , the constant term is .
STEP 7
The **leading term** is the term with the highest power of when the polynomial is in standard form.
In our standard form polynomial , the leading term is .
STEP 8
The **leading coefficient** is the number multiplying the highest power of in the leading term.
In our leading term , the leading coefficient is **-9**.
STEP 9
The expression represents a **quartic** polynomial with **four** terms.
The constant term is , the leading term is , and the leading coefficient is **-9**.
Was this helpful?