Polynomial: Definition (One Variable) MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz focuses on Unit II: Algebra, specifically the definition of polynomials in one variable. It covers valid polynomials, counterexamples (non-polynomials), coefficients, and degrees. Review the concepts, identify the correct expressions, and click “Submit Quiz” to check your score. You can also download the detailed answer key PDF for revision.
Polynomials: Definition and Concepts
In Class 9 Mathematics, under Unit II: Algebra, a polynomial in one variable is an algebraic expression of the form p(x) where the exponents of the variable are always whole numbers (non-negative integers). Examples include x^2 + 2x, 3y^3 – 5, and t + 1.
1. Conditions for a Polynomial
An expression is NOT a polynomial if:
- The variable has a negative exponent (e.g., 1/x or x^-1).
- The variable is inside a root (e.g., square root of x), meaning a fractional exponent.
- The variable appears in the denominator.
Example: x + 1/x is not a polynomial because 1/x is x^-1 (negative power).
2. Key Terms
- Terms: The parts of a polynomial separated by + or – signs.
- Coefficient: The number multiplied by the variable (e.g., in -5x^2, the coefficient is -5).
- Constant Polynomial: A polynomial consisting of only a number (e.g., 7 or -2). Its degree is 0.
- Zero Polynomial: The number 0 is called the zero polynomial. Its degree is not defined.
3. Classification by Terms
| Type | Definition | Example |
|---|---|---|
| Monomial | One term | 2x, 5x^2 |
| Binomial | Two terms | x + 1, x^2 – 4 |
| Trinomial | Three terms | x^2 + 2x + 1 |
Extra Practice Questions
- Identify if y^2 + square root of 2 is a polynomial. (Answer: Yes, because the variable y has a whole number power. The root is on the constant, not the variable.)
- What is the degree of the polynomial 4x^3 – 2x + 1? (Answer: 3)
- Give an example of a binomial of degree 35. (Answer: x^35 + 10)
- Is 0 a polynomial? (Answer: Yes, it is the Zero Polynomial).
- Write the coefficient of x^2 in: 2 – x^2 + x^3. (Answer: -1)
