Questions: Which algebraic expression is a trinomial? (x^3+x^2-sqrtx) (2 x^3-x^2) (4 x^3+x^2-frac1x) (x^6-x+sqrt6)

$Which algebraic expression is a trinomial? (x^3+x^2-sqrtx) (2 x^3-x^2) (4 x^3+x^2-frac1x) (x^6-x+sqrt6)$

Transcript text: Which algebraic expression is a trinomial? $x^{3}+x^{2}-\sqrt{x}$ $2 x^{3}-x^{2}$ $4 x^{3}+x^{2}-\frac{1}{x}$ $x^{6}-x+\sqrt{6}$

Solution

Solution Steps

To determine which algebraic expression is a trinomial, we need to identify the expression that consists of exactly three terms. A trinomial is a polynomial with three terms, where each term is a product of a constant and a variable raised to a non-negative integer power.

Step 1: Identify the Number of Terms in Each Expression

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

Step 2: Analyze Each Expression

$ x^3 + x^2 - \sqrt{x} $: This expression has three terms: $ x^3 $, $ x^2 $, and $ -\sqrt{x} $.
$ 2x^3 - x^2 $: This expression has two terms: $ 2x^3 $ and $ -x^2 $.
$ 4x^3 + x^2 - \frac{1}{x} $: This expression has three terms: $ 4x^3 $, $ x^2 $, and $ -\frac{1}{x} $.
$ x^6 - x + \sqrt{6} $: This expression has three terms: $ x^6 $, $ -x $, and $ \sqrt{6} $.

Step 3: Determine Which Expression is a Trinomial

From the analysis, the expressions $ x^3 + x^2 - \sqrt{x} $, $ 4x^3 + x^2 - \frac{1}{x} $, and $ x^6 - x + \sqrt{6} $ each have three terms, making them trinomials.