Classify the expression $7x$ as monomial, binomial, trinomial, polynomial, or multinomial.
Classify the expression $3x + 5$.
Classify the expression $4a + 3b – 2$.
Classify the expression $x^{2} + x + 1$.
Classify the expression $6x^{3}y$.
Classify the expression $2x + 3y – z + 5$.
Which type of algebraic expression is $5x – 4y$?
Identify whether $2 + \frac{3}{x}$ is a polynomial or a multinomial.
Write one example each of a monomial and a binomial.
Write one example each of a trinomial and a polynomial.
1. 7x: Monomial
Explanation: A monomial is an expression consisting of only one term. Since $7x$ is a single product with no addition or subtraction signs separating it from other terms, it is a monomial.
2. 3x + 5: Binomial
Explanation: A binomial consists of two terms. Here, $3x$ is the first term and $5$ is the second term, joined by an addition sign.
3. 4a + 3b – 2: Trinomial
Explanation: A trinomial contains three terms. In this expression, the terms are $4a$, $3b$, and $-2$.
4. x² + x + 1: Trinomial
Explanation: Similar to the previous problem, this expression has three distinct terms ($x^2$, $x$, and $1$).
5. 6x³y: Monomial
Explanation: Even though there are multiple variables ($x$ and $y$) and an exponent, there is no addition or subtraction separating them. It remains a single term.
6. 2x + 3y – z + 5: Multinomial
Explanation: A multinomial is an algebraic expression with two or more terms. While this is also a polynomial, “multinomial” is a broad classification for any expression with many terms (in this case, four).
7. 5x – 4y: Binomial
Explanation: This expression contains two terms ($5x$ and $-4y$) separated by a subtraction sign.
8. 2 + 3/x: Multinomial
Explanation: This is a multinomial because it has two terms. However, it is not a polynomial because one of the terms has a variable in the denominator ($3/x$ is $3x^{-1}$), and polynomials must have non-negative integer exponents.
9. Monomial: 5y; Binomial: x + 2
Explanation: $5y$ represents a single term, while $x + 2$ represents two terms joined by an operator.
10. Trinomial: a² + 2a + 1; Polynomial: x³ + 3x² + 3x + 1
Explanation: The trinomial has exactly three terms. The polynomial example provided has four terms, all with non-negative integer exponents.