Question
Find the degree of the following polynomial: \[ -7+2 x-3 x^{2}+x^{3} \] Provide your answer below:
Ask by Colon Ryan. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The degree of the polynomial is 3.
Solution
**Step 1:** Write down the polynomial:
\[
-7 + 2x - 3x^2 + x^3
\]
**Step 2:** Identify the degree of each term:
- The term \(-7\) has degree \(0\).
- The term \(2x\) has degree \(1\).
- The term \(-3x^2\) has degree \(2\).
- The term \(x^3\) has degree \(3\).
**Step 3:** The degree of the polynomial is the highest degree among all the terms, which is \(3\).
**Final Answer:** \(3\)
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Simplify this solution The Deep Dive
To determine the degree of the polynomial \( -7 + 2x - 3x^2 + x^3 \), we look for the highest exponent of the variable \( x \). The term with the highest degree here is \( x^3 \). Therefore, the degree of the polynomial is 3. In summary, the degree of the polynomial \( -7 + 2x - 3x^2 + x^3 \) is \( \boxed{3} \).
