Coefficients and Terms of Polynomial MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz focuses on Unit II: Algebra. It specifically covers the identification of coefficients, counting terms, and distinguishing like and unlike terms in the context of polynomials. Test your understanding of these fundamental algebraic concepts, check your score instantly, and download a PDF solution sheet for revision.
Understanding Coefficients and Terms in Polynomials
In Class 9 Mathematics, Unit II: Algebra introduces the fundamental building blocks of polynomials. A clear understanding of terms and coefficients is essential for performing algebraic operations like addition, subtraction, and factorization. This section breaks down these concepts.
1. What are Terms?
A polynomial is made up of parts called terms. Terms are separated by plus (+) or minus (-) signs. Each term consists of variables and coefficients (numbers).
- Example: In the polynomial 4x^2 – 3x + 7, there are three terms: 4x^2, -3x, and 7.
- Note that the sign preceding the term is part of the term itself.
2. What is a Coefficient?
A coefficient is the numerical factor of a term containing a variable. It is the number multiplied by the variable.
- In the term 5x^3, the coefficient of x^3 is 5.
- In the term -x, the coefficient of x is -1 (since -x is the same as -1 multiplied by x).
- In the term x^2, the coefficient is 1.
- Zero Coefficient: If a specific power of a variable is missing, its coefficient is 0. For example, in 2x + 5, the coefficient of x^2 is 0.
3. Constant Terms
A term that does not contain any variable is called a constant term. For example, in the polynomial x^2 + 5x – 9, the constant term is -9. It can also be viewed as the coefficient of x^0.
Types of Polynomials Based on Terms
| Type | Definition | Example |
|---|---|---|
| Monomial | A polynomial with exactly one term. | 3x, -5y^2, 7 |
| Binomial | A polynomial with exactly two terms. | x + 2, 4y^2 – y |
| Trinomial | A polynomial with exactly three terms. | x^2 – 3x + 5 |
Quick Revision Points
- Terms are separated by + or – operators. Multiplied factors (like 3xy) form a single term.
- Always include the sign (positive or negative) when identifying a coefficient or a term.
- Like terms have the same variable raised to the same power (e.g., 2x^2 and -5x^2). Only like terms can be added or subtracted.
Extra Practice Questions
- Write the coefficient of x in the polynomial: 2 – x + x^2. (Answer: -1)
- How many terms are in the expression 5x * 2y? (Answer: 1, because it simplifies to 10xy)
- Identify the constant term in: x^3 – 5. (Answer: -5)
- What is the coefficient of x^2 in the polynomial 5x + 7? (Answer: 0)
- Classify 3x^2 – x as a monomial, binomial, or trinomial. (Answer: Binomial)
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