Which algebraic expression is a trinomial?

A. [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex]
B. [tex]\( 2x^3 - x^2 \)[/tex]
C. [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex]
D. [tex]\( x^6 - x + \sqrt{6} \)[/tex]



Answer :

To determine which algebraic expression is a trinomial, we need to count the number of terms in each expression. A trinomial is defined as a polynomial with exactly three terms.

Let's analyze each given expression step-by-step.

1. [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex]

This expression consists of three terms:
1) [tex]\( x^3 \)[/tex]
2) [tex]\( x^2 \)[/tex]
3) [tex]\( -\sqrt{x} \)[/tex]

Thus, the expression [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex] has 3 terms.

2. [tex]\( 2x^3 - x^2 \)[/tex]

This expression consists of two terms:
1) [tex]\( 2x^3 \)[/tex]
2) [tex]\( -x^2 \)[/tex]

Thus, the expression [tex]\( 2x^3 - x^2 \)[/tex] has 2 terms.

3. [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex]

This expression consists of three terms:
1) [tex]\( 4x^3 \)[/tex]
2) [tex]\( x^2 \)[/tex]
3) [tex]\( -\frac{1}{x} \)[/tex]

Thus, the expression [tex]\( 4x^3 + x^2 - \frac{1}{x} \)[/tex] has 3 terms.

4. [tex]\( x^6 - x + \sqrt{6} \)[/tex]

This expression consists of three terms:
1) [tex]\( x^6 \)[/tex]
2) [tex]\( -x \)[/tex]
3) [tex]\( \sqrt{6} \)[/tex]

Thus, the expression [tex]\( x^6 - x + \sqrt{6} \)[/tex] has 3 terms.

From the analysis, the expressions with exactly three terms (trinomials) 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]

The expression that is the first trigonomial in the given list is:
[tex]\[ x^3 + x^2 - \sqrt{x} \][/tex]

Therefore, the algebraic expression [tex]\( x^3 + x^2 - \sqrt{x} \)[/tex] is the first trinomial in the given list.