Question
Answer the questions about the following polynomial.
minus, 2, minus, start fraction, x, divided by, 3, end fraction
−2−
3
x
The expression represents a _____ polynomial with ____terms. The constant term is
____, the leading term is _____, and the leading coefficient is___.
quartic, cubic, linear, quadratic, quintic
minus, 2, minus, start fraction, x, divided by, 3, end fraction
−2−
3
x
The expression represents a _____ polynomial with ____terms. The constant term is
____, the leading term is _____, and the leading coefficient is___.
quartic, cubic, linear, quadratic, quintic
Answers
GPT-4o mini
Let's analyze the given polynomial expression:
\[
-2 - \frac{x}{3}
\]
1. **Identify the degree of the polynomial**: The highest degree of \(x\) in the expression \(-\frac{x}{3}\) is 1, which means this is a linear polynomial.
2. **Count the terms**: The polynomial consists of two terms: \(-2\) (the constant term) and \(-\frac{x}{3}\) (the \(x\) term). Therefore, it has 2 terms.
3. **Identify the constant term**: The constant term is \(-2\).
4. **Identify the leading term**: The leading term is the term with the highest degree, which is \(-\frac{x}{3}\).
5. **Identify the leading coefficient**: The leading coefficient is the coefficient of the leading term. In this case, the leading term is \(-\frac{x}{3}\), so the leading coefficient is \(-\frac{1}{3}\).
Now we can fill in the blanks:
The expression represents a **linear** polynomial with **2** terms. The constant term is **−2**, the leading term is **−\frac{x}{3}**, and the leading coefficient is **−\frac{1}{3}**.
\[
-2 - \frac{x}{3}
\]
1. **Identify the degree of the polynomial**: The highest degree of \(x\) in the expression \(-\frac{x}{3}\) is 1, which means this is a linear polynomial.
2. **Count the terms**: The polynomial consists of two terms: \(-2\) (the constant term) and \(-\frac{x}{3}\) (the \(x\) term). Therefore, it has 2 terms.
3. **Identify the constant term**: The constant term is \(-2\).
4. **Identify the leading term**: The leading term is the term with the highest degree, which is \(-\frac{x}{3}\).
5. **Identify the leading coefficient**: The leading coefficient is the coefficient of the leading term. In this case, the leading term is \(-\frac{x}{3}\), so the leading coefficient is \(-\frac{1}{3}\).
Now we can fill in the blanks:
The expression represents a **linear** polynomial with **2** terms. The constant term is **−2**, the leading term is **−\frac{x}{3}**, and the leading coefficient is **−\frac{1}{3}**.