Trinomial Identification

An algebraic expression is made up of terms. Terms are separated by addition (+) or subtraction (-) signs. Polynomials are algebraic expressions where the variables have non-negative integer exponents. Polynomials are classified based on the number of terms they contain:

• Monomial: A polynomial with exactly one term.
• Binomial: A polynomial with exactly two terms.
• Trinomial: A polynomial with exactly three terms.
• Polynomial: An expression with one or more terms.

Identifying the Number of Terms in Each Option

Let's examine each given option to determine the number of terms it has:

1. \(\frac{7}{5}\) p²q⁵r³

   This expression has only one term: \(\frac{7}{5} p^2 q^5 r^3\). Therefore, it is a monomial.

2. p ²q ⁵r³+p⁷q⁵r³- p²q³r²+p²q²r³

   This expression has four terms: \(p^2 q^5 r^3\), \(+p^7 q^5 r^3\), \(-p^2 q^3 r^2\), and \(+p^2 q^2 r^3\). Therefore, it is a polynomial with four terms.

3. 9x ²+ yz ²q⁵r³

   This expression has two terms: \(9x^2\) and \(+yz^2 q^5 r^3\). Therefore, it is a binomial.

4. x ²y + 9x²+ 5yz²

   This expression has three terms: \(x^2 y\), \(+9x^2\), and \(+5yz^2\). Therefore, it is a trinomial.

Trinomial Identification Conclusion

Based on the analysis, the expression with exactly three terms is \(x^2 y + 9x^2 + 5yz^2\). This is the definition of a trinomial.