Question
Consider the algebraic expression \( 9-20 x^{4} \). What is the degree of this polynomial? Identify the constant term. Identify the leading coefficient. Identify the leading term.
Ask by Huang Carter. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
- **Degree:** 4
- **Constant Term:** 9
- **Leading Coefficient:** -20
- **Leading Term:** -20x⁴
Solution
1. The polynomial is given as \( 9 - 20x^4 \). To determine its degree, rewrite it in standard form (descending order of exponents):
\[
-20x^4 + 9
\]
The term with the highest exponent is \( -20x^4 \), and its exponent is \( 4 \).
**Degree:** \( 4 \).
2. The constant term in a polynomial is the term that does not contain any variable; in this expression, it is:
\[
9
\]
**Constant Term:** \( 9 \).
3. The leading coefficient is the coefficient of the term with the highest degree. Since the leading term is \( -20x^4 \), the coefficient is:
\[
-20
\]
**Leading Coefficient:** \( -20 \).
4. The leading term is the term with the highest degree in the polynomial. In standard form, it is:
\[
-20x^4
\]
**Leading Term:** \( -20x^4 \).
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Beyond the Answer
The degree of the polynomial \( 9 - 20x^{4} \) is determined by the highest exponent of the variable, which in this case is 4. So, the degree is 4. The constant term is the term in the expression that does not contain any variables, which is 9. The leading coefficient is the coefficient of the leading term, which is \(-20\) associated with \(x^4\). The leading term of the polynomial is the term with the highest degree, which is \(-20x^4\).