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Quizzes > Mathematics

Monomial binomial or trinomial? Take the quiz to classify polynomials

Quick, free polynomial types quiz. Instant results.

Editorial: Review CompletedCreated By: Shreya BiswasUpdated Aug 26, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
paper art illustration of algebraic expressions monomials binomials polynomials on coral background quiz promotion

This quiz helps you tell whether each expression is a monomial, binomial, or trinomial and build speed classifying polynomials. After you finish, try a quick polynomial quiz, sharpen factoring with our polynomials and factoring quiz, or review basics in a combine like terms quiz.

What type of polynomial is 5x^2?
Polynomial
Monomial
Binomial
Trinomial
The expression 5x^2 has only one term and a nonzero coefficient, which is the definition of a monomial. A binomial has two terms and a trinomial has three terms. While a monomial is also a polynomial, the specific classification is based on the number of terms. Therefore, 5x^2 is classified as a monomial.
What type of polynomial is x + 3?
Monomial
Trinomial
Binomial
Linear
The expression x + 3 has two distinct terms, which defines a binomial. A monomial has only one term, and a trinomial has three terms. The term "linear" describes the degree of the polynomial, not its number of terms. Therefore, x + 3 is specifically a binomial.
What type of polynomial is the constant 7?
Binomial
Trinomial
Zero polynomial
Monomial
The constant 7 is a single term with no variables, fitting the definition of a monomial. A binomial or trinomial would require two or three terms, respectively. The zero polynomial is a special case where all coefficients are zero, which does not apply here. Therefore, 7 is classified as a monomial.
What type of polynomial is x^3 - 2x + 5?
Monomial
Quartic
Trinomial
Binomial
The expression x^3 - 2x + 5 contains three nonzero terms, which defines a trinomial. A monomial has one term and a binomial has two terms. The term 'quartic' refers to a polynomial of degree four, not the number of terms. Therefore, x^3 - 2x + 5 is a trinomial.
After combining like terms, classify the expression 2x^2 + 4x^2 - 3x + 7.
Monomial
Quadratic
Binomial
Trinomial
First, combine like terms: 2x^2 + 4x^2 simplifies to 6x^2, giving 6x^2 - 3x + 7. This expression has three nonzero terms, which defines a trinomial. While the expression is a quadratic polynomial by degree, the classification here is based on the number of terms. Therefore, the simplified form is a trinomial.
What type of polynomial is 0x^3 + 5x after simplifying?
Trinomial
Monomial
Polynomial
Binomial
The term 0x^3 evaluates to zero and is removed, leaving only 5x. Zero coefficients do not contribute to the count of terms. An expression with a single nonzero term is classified as a monomial. Although it is also a polynomial, the specific classification by term count makes it a monomial.
How would you classify the expression -2ab + 3a^2b^2?
Polynomial
Monomial
Binomial
Trinomial
The expression -2ab + 3a^2b^2 consists of exactly two nonzero terms, which defines a binomial. A monomial has one term, and a trinomial has three terms. While every binomial is also a polynomial, the precise term count classification is binomial.
Which of the following is a trinomial?
x^2 + 5x + 6
x^2 + 2x^3
7y^3
3x - 4
The expression x^2 + 5x + 6 has three terms, meeting the definition of a trinomial. The expression 3x - 4 has two terms (binomial), 7y^3 has one term (monomial), and x^2 + 2x^3 also has two terms. Classification is strictly based on the number of nonzero terms.
Classify the polynomial 3x^3 + 0x^2 + x + 0.
Binomial
Monomial
Polynomial
Trinomial
Zero coefficient terms do not contribute to the number of terms, so 0x^2 and 0 are removed, leaving 3x^3 + x. Combining nonzero terms is key to classification. This expression has two terms, defining it as a binomial. While it is indeed a polynomial, the classification by term count makes it a binomial.
After expanding (x + 2)(x - 2), what type of polynomial results?
Binomial
Trinomial
Quadratic
Monomial
Expanding (x + 2)(x - 2) gives x^2 - 4, which contains two terms (x^2 and -4). An expression with two nonzero terms is a binomial. Although its degree is quadratic, the classification here refers to the number of terms. Therefore, the result is a binomial.
If p(x) = 2x^3 + 4x - 5 + x^3, what is the classification after combining like terms?
Trinomial
Binomial
Monomial
Polynomial
Combine like terms: 2x^3 + x^3 becomes 3x^3, so p(x) simplifies to 3x^3 + 4x - 5. Combining like terms ensures accurate counting of terms. This simplified form has three nonzero terms, defining it as a trinomial. While it is also a polynomial, the specific term count classification is trinomial.
Simplify the expression 5(x - 1) + 2(x + 3) and classify the result.
Monomial
Quadratic
Binomial
Trinomial
First, distribute: 5(x - 1) + 2(x + 3) becomes 5x - 5 + 2x + 6, which simplifies to 7x + 1. This expression has two nonzero terms, defining it as a binomial. Quadratic refers to degree two, which does not apply here. Thus, the result is a binomial.
What is the classification by term count of f(x) = x^5 - x^4 + x^3 - x^2 + x - 1?
Monomial
Polynomial
Binomial
Trinomial
The function f(x) contains six nonzero terms, exceeding the three-term limit for trinomials. Monomials, binomials, and trinomials are specific cases of polynomials with one, two, and three terms respectively. Any polynomial with more than three terms is simply classified as a polynomial without a special term count name. Therefore, f(x) is classified as a polynomial.
Classify the simplified form of P(x) = 3x^2(x - 1) + 2x(x^2 + 1).
Trinomial
Monomial
Binomial
Polynomial
First expand and combine like terms: 3x^2(x - 1) + 2x(x^2 + 1) simplifies to 3x^3 - 3x^2 + 2x^3 + 2x = 5x^3 - 3x^2 + 2x. Identifying like terms ensures accurate classification. This result has three nonzero terms, defining it as a trinomial. Although it is a polynomial, classification by term count is trinomial.
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Study Outcomes

  1. Identify Monomial Expressions -

    Recognize and categorize single-term expressions as monomials to build a foundation in polynomial classification.

  2. Distinguish Binomial Expressions -

    Differentiate two-term algebraic expressions from other polynomials by identifying binomial structures accurately.

  3. Classify Trinomial Expressions -

    Analyze three-term algebraic expressions and correctly classify them as trinomials.

  4. Differentiate Polynomials by Term Count -

    Apply clear criteria based on the number of terms to classify monomials, binomials, and trinomials confidently.

  5. Analyze Polynomial Structures -

    Evaluate mixed expressions and determine whether they are monomial, binomial, or trinomial polynomials.

  6. Self-Assess Polynomial Classification Skills -

    Use quiz feedback to gauge mastery of polynomial terminology and identify areas for further practice.

Cheat Sheet

  1. Term Count Classification -

    Remember that a monomial has one term, a binomial has two terms, and a trinomial has three terms. Use the mnemonic "mono-1, bi-2, tri-3" to quickly distinguish monomial, binomial and trinomial expressions such as 5x², x+7, and 3x²−2x+1. (Source: Khan Academy)

  2. Degree-Based Naming -

    Polynomials are also classified by degree: a constant polynomial (degree 0), linear (degree 1), quadratic (degree 2), cubic (degree 3), and so on. For instance, 4 is constant, 2x−5 is linear, and x²+3x+2 is a quadratic trinomial. (Source: MIT OpenCourseWare)

  3. Standard Form and Ordering -

    Always write polynomials in descending exponent order for consistency: e.g., 2x³−x+4 instead of −x+4+2x³. This standard form makes it easier to spot polynomials, monomials, binomials or trinomials at a glance. (Source: University of Illinois)

  4. Combining Like Terms -

    When adding or subtracting expressions, combine like terms (same variable and exponent) to classify the result correctly. For example, (3x+2)+(5x−4) becomes 8x−2, a binomial, not two separate monomials. (Source: Purplemath)

  5. Recognizing Special Binomial Forms -

    Familiarize yourself with notable binomial expansions like (a+b)² = a² + 2ab + b² and the difference of squares a²−b² = (a−b)(a+b). Spotting these patterns helps you identify binomials and trinomials instantly. (Source: Coursera)

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