Let's classify each given polynomial as a monomial, binomial, or trinomial by first combining like terms:
1. Polynomial: [tex]\(x^3 + 3x^3 + 2x\)[/tex]
- Combine like terms:
- [tex]\(x^3 + 3x^3 = 4x^3\)[/tex]
- There is no need to combine [tex]\(2x\)[/tex] with any other term.
- Combined form: [tex]\(4x^3 + 2x\)[/tex]
- This polynomial has two distinct terms: [tex]\(4x^3\)[/tex] and [tex]\(2x\)[/tex].
Classification: Binomial
2. Polynomial: [tex]\(2x^3 + 5x + 3x^4 - x\)[/tex]
- Combine like terms:
- [tex]\(2x^3\)[/tex] remains as is, since there are no other [tex]\(x^3\)[/tex] terms.
- [tex]\(5x - x = 4x\)[/tex]
- [tex]\(3x^4\)[/tex] remains as is, since there are no other [tex]\(x^4\)[/tex] terms.
- Combined form: [tex]\(3x^4 + 2x^3 + 4x\)[/tex]
- This polynomial has three distinct terms: [tex]\(3x^4\)[/tex], [tex]\(2x^3\)[/tex], and [tex]\(4x\)[/tex].
Classification: Trinomial
3. Polynomial: [tex]\(4x - 5x + x - 2\)[/tex]
- Combine like terms:
- [tex]\(4x - 5x + x = 0x\)[/tex], since [tex]\(4x - 5x + x\)[/tex] cancels out to zero.
- The remaining term is [tex]\(-2\)[/tex].
- Combined form: [tex]\(-2\)[/tex]
- This polynomial has only one term: [tex]\(-2\)[/tex].
Classification: Monomial
4. Polynomial: [tex]\(6x^2 + 5 - 2x^2 - 9\)[/tex]
- Combine like terms:
- [tex]\(6x^2 - 2x^2 = 4x^2\)[/tex]
- [tex]\(5 - 9 = -4\)[/tex]
- Combined form: [tex]\(4x^2 - 4\)[/tex]
- This polynomial has two distinct terms: [tex]\(4x^2\)[/tex] and [tex]\(-4\)[/tex].
Classification: Binomial
In conclusion, the classifications are:
1. Binomial
2. Trinomial
3. Monomial
4. Binomial
