A trinomial is an algebraic expression composed of exactly three terms. Let's analyze each of the given expressions to determine which one qualifies as a trinomial.
1. [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex]
- This expression includes three distinct terms: [tex]\( x^3 \)[/tex], [tex]\( x^2 \)[/tex], and [tex]\( -\sqrt{x} \)[/tex].
- Therefore, it has 3 terms.
2. [tex]\( 2x^3 - x^2 \)[/tex]
- This expression includes only two distinct terms: [tex]\( 2x^3 \)[/tex] and [tex]\( -x^2 \)[/tex].
- Therefore, it has 2 terms.
3. [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex]
- This expression includes three distinct terms: [tex]\( 4x^3 \)[/tex], [tex]\( x^2 \)[/tex], and [tex]\( -\frac{1}{x} \)[/tex].
- Therefore, it has 3 terms.
4. [tex]\( x^6 - x + \sqrt{6} \)[/tex]
- This expression includes three distinct terms: [tex]\( x^6 \)[/tex], [tex]\( -x \)[/tex], and [tex]\( \sqrt{6} \)[/tex].
- Therefore, it has 3 terms.
To summarize:
- [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex]: 3 terms
- [tex]\( 2x^3 - x^2 \)[/tex]: 2 terms
- [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex]: 3 terms
- [tex]\( x^6 - x + \sqrt{6} \)[/tex]: 3 terms
Expressions containing three terms (trinomials) here are:
- [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex]
- [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex]
- [tex]\( x^6 - x + \sqrt{6} \)[/tex]
So, the algebraic expressions that are trinomials are:
1. [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex]
3. [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex]
4. [tex]\( x^6 - x + \sqrt{6} \)[/tex]
