Get personalized and accurate responses to your questions with IDNLearn.com. Get comprehensive answers to all your questions from our network of experienced experts.
Sagot :
To determine the correct statement about the polynomial [tex]\( 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \)[/tex] after it has been fully simplified, let's proceed step-by-step with the simplification process.
### Step-by-Step Simplification:
1. Write down the polynomial:
[tex]\[ 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \][/tex]
2. Combine like terms:
- Notice that [tex]\( 3x^2y^2 \)[/tex] and [tex]\( -3x^2y^2 \)[/tex] are like terms and can be combined:
[tex]\[ 3x^2y^2 - 3x^2y^2 = 0 \][/tex]
- After combining these terms, the polynomial simplifies to:
[tex]\[ 0 - 5xy^2 + 2x^2 \][/tex]
Which is:
[tex]\[ -5xy^2 + 2x^2 \][/tex]
3. Count the remaining terms:
- The simplified polynomial [tex]\( -5xy^2 + 2x^2 \)[/tex] consists of 2 terms: [tex]\( -5xy^2 \)[/tex] and [tex]\( 2x^2 \)[/tex].
4. Determine the degree of the polynomial:
- The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
- For the term [tex]\( -5xy^2 \)[/tex]:
- The degree is [tex]\( 1 \)[/tex] (from [tex]\( x \)[/tex]) + [tex]\( 2 \)[/tex] (from [tex]\( y^2 \)[/tex]) = [tex]\( 3 \)[/tex].
- For the term [tex]\( 2x^2 \)[/tex]:
- The degree is [tex]\( 2 \)[/tex] (from [tex]\( x^2 \)[/tex]).
- The degree of the polynomial is the highest degree of its terms, which in this case is [tex]\( 3 \)[/tex] (from [tex]\( -5xy^2 \)[/tex]).
### Conclusion:
After fully simplifying the polynomial [tex]\( 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \)[/tex], we have:
- 2 terms: [tex]\( -5xy^2 \)[/tex] and [tex]\( 2x^2 \)[/tex].
- The highest degree term has a degree of [tex]\( 3 \)[/tex].
Therefore, the correct statement is:
It has 2 terms and a degree of 3.
### Step-by-Step Simplification:
1. Write down the polynomial:
[tex]\[ 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \][/tex]
2. Combine like terms:
- Notice that [tex]\( 3x^2y^2 \)[/tex] and [tex]\( -3x^2y^2 \)[/tex] are like terms and can be combined:
[tex]\[ 3x^2y^2 - 3x^2y^2 = 0 \][/tex]
- After combining these terms, the polynomial simplifies to:
[tex]\[ 0 - 5xy^2 + 2x^2 \][/tex]
Which is:
[tex]\[ -5xy^2 + 2x^2 \][/tex]
3. Count the remaining terms:
- The simplified polynomial [tex]\( -5xy^2 + 2x^2 \)[/tex] consists of 2 terms: [tex]\( -5xy^2 \)[/tex] and [tex]\( 2x^2 \)[/tex].
4. Determine the degree of the polynomial:
- The degree of a term in a polynomial is the sum of the exponents of the variables in that term.
- For the term [tex]\( -5xy^2 \)[/tex]:
- The degree is [tex]\( 1 \)[/tex] (from [tex]\( x \)[/tex]) + [tex]\( 2 \)[/tex] (from [tex]\( y^2 \)[/tex]) = [tex]\( 3 \)[/tex].
- For the term [tex]\( 2x^2 \)[/tex]:
- The degree is [tex]\( 2 \)[/tex] (from [tex]\( x^2 \)[/tex]).
- The degree of the polynomial is the highest degree of its terms, which in this case is [tex]\( 3 \)[/tex] (from [tex]\( -5xy^2 \)[/tex]).
### Conclusion:
After fully simplifying the polynomial [tex]\( 3x^2y^2 - 5xy^2 - 3x^2y^2 + 2x^2 \)[/tex], we have:
- 2 terms: [tex]\( -5xy^2 \)[/tex] and [tex]\( 2x^2 \)[/tex].
- The highest degree term has a degree of [tex]\( 3 \)[/tex].
Therefore, the correct statement is:
It has 2 terms and 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 answers ends at IDNLearn.com. Thanks for visiting, and we look forward to helping you again soon.