Monomial, binomial, trinomial: Definitions and real-world examples.

📚 Quick Study Guide

• 🔢 A monomial is an algebraic expression with only one term. It can be a number, a variable, or the product of numbers and variables. Example: $5$, $x$, $3y^2$, $-7ab$.
• ➕ A binomial is an algebraic expression with two terms separated by a plus or minus sign. Example: $x + 2$, $3y - 5$, $a^2 + b^2$.
• ➗ A trinomial is an algebraic expression with three terms separated by plus or minus signs. Example: $x^2 + 2x + 1$, $a + b - c$, $4p^2 - 3p + 8$.
• 💡 Remember that terms are separated by addition or subtraction, not multiplication or division.
• 📐 These expressions are fundamental in algebra and are used in various mathematical operations such as factoring, simplifying, and solving equations.

✍️ Practice Quiz

1. Which of the following is a monomial?
   1. A. $x + y$
   2. B. $3x^2$
   3. C. $a - b + c$
   4. D. $2p + q - 5$
2. Which of the following is a binomial?
   1. A. $7$
   2. B. $4x^2 - 9$
   3. C. $x^2 + 2x + 1$
   4. D. $5abc$
3. Which of the following is a trinomial?
   1. A. $2x$
   2. B. $a + b$
   3. C. $x^2 - 5x + 6$
   4. D. $9y^3$
4. Identify the type of expression: $5x^3 - 2x$.
   1. A. Monomial
   2. B. Binomial
   3. C. Trinomial
   4. D. None of the above
5. Identify the type of expression: $7y^2 + 3y - 1$.
   1. A. Monomial
   2. B. Binomial
   3. C. Trinomial
   4. D. None of the above
6. Which expression represents the area of a rectangle with length $(x + 3)$ and width $x$?
   1. A. $x$
   2. B. $x + 3$
   3. C. $x^2 + 3x$
   4. D. $2x + 3$
7. Which of the following is NOT a polynomial?
   1. A. $x^2 + 2x + 1$
   2. B. $5y - 3$
   3. C. $4$
   4. D. $\frac{1}{x}$