Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
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.
### 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.
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.