Find expert answers and community insights on IDNLearn.com. Discover comprehensive answers to your questions from our community of knowledgeable experts.
Sagot :
Absolutely, let's analyze each polynomial step-by-step to classify and determine its degree.
### Polynomial: [tex]\( 3x^2 \)[/tex]
1. Form: This polynomial consists of a single term, [tex]\( 3x^2 \)[/tex].
2. Type: A polynomial with only one term is called a monomial.
3. Degree: The degree of a monomial is simply the exponent of the variable. Here the highest exponent of [tex]\(x\)[/tex] is 2.
Therefore, [tex]\( 3x^2 \)[/tex] is a monomial with a degree of 2.
### Polynomial: [tex]\( x^2y + 3xy^2 + 1 \)[/tex]
1. Form: This polynomial consists of three terms: [tex]\( x^2y \)[/tex], [tex]\( 3xy^2 \)[/tex], and 1.
2. Type: A polynomial with three terms is called a trinomial.
3. Degree: For polynomials with multiple variables, the degree of a term is the sum of the exponents of all variables within that term. Let's examine the degree of each term:
- [tex]\( x^2y \)[/tex]: The sum of the exponents is [tex]\( 2 + 1 = 3 \)[/tex].
- [tex]\( 3xy^2 \)[/tex]: The sum of the exponents is [tex]\( 1 + 2 = 3 \)[/tex].
- 1: This is a constant term with a degree of 0.
The degree of the polynomial is the highest degree of its terms. Here, both [tex]\( x^2y \)[/tex] and [tex]\( 3xy^2 \)[/tex] have the highest degree, which is 3.
Therefore, [tex]\( x^2y + 3xy^2 + 1 \)[/tex] is a trinomial with a degree of 3.
### Final Answer:
- The polynomial [tex]\( 3x^2 \)[/tex] is a monomial with a degree of 2.
- The polynomial [tex]\( x^2y + 3xy^2 + 1 \)[/tex] is a trinomial with a degree of 3.
### Polynomial: [tex]\( 3x^2 \)[/tex]
1. Form: This polynomial consists of a single term, [tex]\( 3x^2 \)[/tex].
2. Type: A polynomial with only one term is called a monomial.
3. Degree: The degree of a monomial is simply the exponent of the variable. Here the highest exponent of [tex]\(x\)[/tex] is 2.
Therefore, [tex]\( 3x^2 \)[/tex] is a monomial with a degree of 2.
### Polynomial: [tex]\( x^2y + 3xy^2 + 1 \)[/tex]
1. Form: This polynomial consists of three terms: [tex]\( x^2y \)[/tex], [tex]\( 3xy^2 \)[/tex], and 1.
2. Type: A polynomial with three terms is called a trinomial.
3. Degree: For polynomials with multiple variables, the degree of a term is the sum of the exponents of all variables within that term. Let's examine the degree of each term:
- [tex]\( x^2y \)[/tex]: The sum of the exponents is [tex]\( 2 + 1 = 3 \)[/tex].
- [tex]\( 3xy^2 \)[/tex]: The sum of the exponents is [tex]\( 1 + 2 = 3 \)[/tex].
- 1: This is a constant term with a degree of 0.
The degree of the polynomial is the highest degree of its terms. Here, both [tex]\( x^2y \)[/tex] and [tex]\( 3xy^2 \)[/tex] have the highest degree, which is 3.
Therefore, [tex]\( x^2y + 3xy^2 + 1 \)[/tex] is a trinomial with a degree of 3.
### Final Answer:
- The polynomial [tex]\( 3x^2 \)[/tex] is a monomial with a degree of 2.
- The polynomial [tex]\( x^2y + 3xy^2 + 1 \)[/tex] is a trinomial with a degree of 3.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.