To thoroughly understand and solve the given polynomial expression, let's break it down and analyze it step-by-step.
### Given Polynomial:
[tex]\[ 3x^4 - 11x^2 - 20 \][/tex]
### Step-by-Step Solution:
1. Identify the Degree of the Polynomial:
- The highest power of [tex]\( x \)[/tex] in the polynomial [tex]\( 3x^4 - 11x^2 - 20 \)[/tex] is 4.
- Therefore, this is a 4th-degree polynomial.
2. Breakdown of Terms:
- The polynomial consists of three terms: [tex]\( 3x^4 \)[/tex], [tex]\(-11x^2\)[/tex], and [tex]\(-20\)[/tex].
- These terms include:
- [tex]\( 3x^4 \)[/tex]: A term with [tex]\( x \)[/tex] raised to the power of 4, which is the highest degree term.
- [tex]\( -11x^2 \)[/tex]: A term with [tex]\( x \)[/tex] raised to the power of 2.
- [tex]\( -20 \)[/tex]: A constant term.
3. Understanding the Structure:
- Polynomials of this form can be factored or analyzed for their roots. However, as the instruction suggests, no further calculations should be made, and the expression is taken as it is.
4. Conclusion:
- The polynomial [tex]\( 3x^4 - 11x^2 - 20 \)[/tex] is a 4th-degree polynomial where the coefficients of the terms [tex]\( x^4 \)[/tex] and [tex]\( x^2 \)[/tex] are 3 and -11, respectively, and the constant term is -20.
Thus, the polynomial we've analyzed is:
[tex]\[ 3x^4 - 11x^2 - 20 \][/tex]
This concludes our detailed breakdown of the polynomial expression given.
