which algebraic expression is a trinomial?\n$x^{3}+x^{2}-sqrt{x}$\n$2x^{3}-x^{2}$\n$4x^{3}+x^{2}-\frac{1}{x}$…

which algebraic expression is a trinomial?\n$x^{3}+x^{2}-sqrt{x}$\n$2x^{3}-x^{2}$\n$4x^{3}+x^{2}-\frac{1}{x}$\n$x^{6}-x+sqrt{6}$

which algebraic expression is a trinomial?\n$x^{3}+x^{2}-sqrt{x}$\n$2x^{3}-x^{2}$\n$4x^{3}+x^{2}-\frac{1}{x}$\n$x^{6}-x+sqrt{6}$

Answer

Explanation:

Step1: Recall trinomial definition

A trinomial is a polynomial with three terms where terms are separated by plus or minus signs and each term is a product of a constant and non - negative integer powers of variables.

Step2: Analyze each option

  • Option 1: $x^{3}+x^{2}-\sqrt{x}=x^{3}+x^{2}-x^{\frac{1}{2}}$, has a non - integer power of $x$, not a polynomial.
  • Option 2: $2x^{3}-x^{2}$ has two terms, not a trinomial.
  • Option 3: $4x^{3}+x^{2}-\frac{1}{x}=4x^{3}+x^{2}-x^{- 1}$, has a negative power of $x$, not a polynomial.
  • Option 4: $x^{6}-x+\sqrt{6}$ has three terms and all powers of $x$ are non - negative integers, so it is a trinomial.

Answer:

$x^{6}-x+\sqrt{6}$