Question
Answer the questions about the following polynomial.
minus, 2, x, minus, 8
−2x−8
minus, 2, x, minus, 8
−2x−8
Answers
GPT-4o mini
Sure! Let's analyze the polynomial \( -2x - 8 \).
1. **Degree**: The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of \( x \) is 1 (from \( -2x \)), so the degree of this polynomial is 1.
2. **Leading Coefficient**: The leading coefficient is the coefficient of the term with the highest degree. Here, the leading coefficient is \( -2 \).
3. **Constant Term**: The constant term of the polynomial is the term that does not contain any variables. In this polynomial, the constant term is \( -8 \).
4. **Roots/Zeros**: To find the roots or zeros of the polynomial, we can set it equal to zero and solve for \( x \):
\[
-2x - 8 = 0
\]
Adding 8 to both sides gives:
\[
-2x = 8
\]
Dividing both sides by -2 gives:
\[
x = -4
\]
So the polynomial has one root, which is \( x = -4 \).
5. **End Behavior**: As \( x \) approaches infinity (\( x \to \infty \)), \( -2x \) approaches negative infinity, and as \( x \) approaches negative infinity (\( x \to -\infty \)), \( -2x \) approaches positive infinity. Therefore, the end behavior can be described as:
- As \( x \to \infty \), \( -2x - 8 \to -\infty \).
- As \( x \to -\infty \), \( -2x - 8 \to +\infty \).
If you have any specific questions or further details you'd like to explore, feel free to ask!
1. **Degree**: The degree of a polynomial is the highest power of the variable in the polynomial. In this case, the highest power of \( x \) is 1 (from \( -2x \)), so the degree of this polynomial is 1.
2. **Leading Coefficient**: The leading coefficient is the coefficient of the term with the highest degree. Here, the leading coefficient is \( -2 \).
3. **Constant Term**: The constant term of the polynomial is the term that does not contain any variables. In this polynomial, the constant term is \( -8 \).
4. **Roots/Zeros**: To find the roots or zeros of the polynomial, we can set it equal to zero and solve for \( x \):
\[
-2x - 8 = 0
\]
Adding 8 to both sides gives:
\[
-2x = 8
\]
Dividing both sides by -2 gives:
\[
x = -4
\]
So the polynomial has one root, which is \( x = -4 \).
5. **End Behavior**: As \( x \) approaches infinity (\( x \to \infty \)), \( -2x \) approaches negative infinity, and as \( x \) approaches negative infinity (\( x \to -\infty \)), \( -2x \) approaches positive infinity. Therefore, the end behavior can be described as:
- As \( x \to \infty \), \( -2x - 8 \to -\infty \).
- As \( x \to -\infty \), \( -2x - 8 \to +\infty \).
If you have any specific questions or further details you'd like to explore, feel free to ask!