Important Multiple Choice Questions on Polynomials for Class 9 with Solutions
Practicing Class 9 Maths Chapter 2 Polynomials MCQs boosts your confidence and helps you master core algebra topics, especially for CBSE and exam preparation. This page provides a well-structured set of multiple-choice questions on polynomials, along with clear solutions and explanations. Use these MCQs to test your understanding, identify knowledge gaps, and improve your speed.
Understanding Class 9 Maths Chapter 2 Polynomials MCQs
A polynomial is an algebraic expression made up of one or more terms, each term consisting of variables raised to whole number exponents and multiplied by coefficients. Polynomials are widely used in mathematics for expressing equations, problem-solving, and representing real-world scenarios. The MCQ format challenges students on key concepts such as the degree of a polynomial, types of polynomials (monomial, binomial, trinomial), zeroes, and value calculations.
Key Concepts of Polynomials for Class 9
Before starting MCQ practice, revise these core ideas:
2. Degree of a polynomial is the highest power of its variable.
3. Types: Monomial (one term), Binomial (two terms), Trinomial (three terms).
4. Constant polynomials have no variable (degree 0), like 5.
5. Zeroes (roots) of a polynomial are the values of the variable for which the polynomial equals zero.
Class 9 Maths Chapter 2 Polynomials MCQs with Answers
Practice these representative MCQs. Answers and explanations are provided for step-by-step learning.
a) One Variable b) Two Variables c) Three Variables d) None
Answer: a
Explanation: It only has powers of x; hence, one variable.
2. The coefficient of \( x^2 \) in \( 3x^3 + 2x^2 - x + 1 \) is:
a) 1 b) 2 c) 3 d) -1
Answer: b
Explanation: The term with \( x^2 \) is 2\( x^2 \), so the coefficient is 2.
3. The degree of \( 4x^3 - 12x^2 + 3x + 9 \) is:
a) 0 b) 1 c) 2 d) 3
Answer: d
Explanation: Highest variable exponent is 3.
4. What is the zero of the polynomial \( f(x) = 2x + 7 \)?
a) \( 2/7 \) b) \( -2/7 \) c) \( 7/2 \) d) \( -7/2 \)
Answer: d
Step 1: Set \( f(x) = 0 \): \( 2x + 7 = 0 \)
Step 2: \( 2x = -7 \)
Step 3: \( x = -7/2 \)
5. Which of the following is a constant polynomial?
a) 4x + 1 b) 3 c) 2x\(^2\) d) 6x + 3
Answer: b
Explanation: Only 3 has degree 0 (no variable).
Polynomials Practice Table for Quick Revision
Here are sample polynomials and their properties for revision:
| Polynomial | Type | Degree |
|---|---|---|
| 7x | Monomial | 1 |
| 3x2 - 2x | Binomial | 2 |
| 2x3 + x - 1 | Trinomial | 3 |
| 5 | Constant | 0 |
Understanding the type and degree helps answer MCQs quickly.
Mistakes to Avoid With Polynomials MCQs
- Confusing the polynomial’s highest coefficient with its degree.
- Mixing up terms like zero (root) and coefficient.
- Not checking if all exponents are whole numbers (otherwise, it’s not a polynomial).
Tips for Solving Chapter 2 Polynomials MCQs Faster
- Underline key words like "degree," "coefficient," or "zero" in each question.
- Plug values into polynomials step-by-step for value/zero problems.
- Quickly scan options for degree and type questions.
Advance Your Polynomial Skills (Related Study Links)
- Polynomial: Find basic concepts and definitions.
- Degree of Polynomial: Deepen your understanding of how to find the degree.
- Factoring Polynomials: Useful for MCQs on factorization and solving roots.
- Remainder Theorem: For solving value problems in MCQs.
- Algebraic Expression: Connects expressions to polynomials in exam questions.
- Monomial in Maths: To clarify monomial, binomial, trinomial differences.
- Polynomials in One Variable: Directly targets exam MCQs.
- Polynomial Division: For advanced factor and division questions.
- Algebraic Equations: Explore how polynomials connect to equations.
- Quadratics: For linking polynomial questions with quadratic equations.
Page Summary
This page covered important Class 9 Maths Chapter 2 Polynomials MCQs for CBSE, explained core concepts, offered multiple question types, and gave direct links for further reading and practice. With regular practice on these polynomials MCQs and related concept links from Vedantu, you will master algebra basics for exams and real-life problem solving.
FAQs on Class 9 Maths Chapter 2 Polynomials MCQs and Concept Practice
1. What is a polynomial in Class 9 Maths Chapter 2?
A polynomial is an algebraic expression made up of variables and constants combined using addition, subtraction, and multiplication, with whole number exponents. In Class 9 Maths Chapter 2 (Polynomials), a polynomial in one variable is written as:
anxⁿ + an-1xⁿ⁻¹ + ... + a1x + a0
Where:
- x is the variable
- n is a non-negative integer
- a0, a1, a2, ... are real numbers (coefficients)
2. What are the different types of polynomials based on degree?
Polynomials are classified based on their degree, which is the highest power of the variable in the expression. The main types are:
- Zero polynomial: Degree is not defined (all coefficients are zero)
- Constant polynomial: Degree 0 (Example: 5)
- Linear polynomial: Degree 1 (Example: 2x + 3)
- Quadratic polynomial: Degree 2 (Example: x² + 4x + 1)
- Cubic polynomial: Degree 3 (Example: x³ - 2x² + x)
3. What is the degree of a polynomial?
The degree of a polynomial is the highest power of the variable in the polynomial. To find it:
- Arrange the polynomial in descending powers.
- Identify the term with the highest exponent.
4. What is a zero of a polynomial?
A zero of a polynomial is the value of the variable that makes the polynomial equal to zero. If p(x) is a polynomial, then a number a is a zero if p(a) = 0.
Example: For p(x) = x - 3,
- Put x = 3
- p(3) = 3 - 3 = 0
5. How do you find the zero of a linear polynomial?
To find the zero of a linear polynomial ax + b, use the formula x = -b/a. Steps:
- Set the polynomial equal to zero: ax + b = 0
- Move constant term: ax = -b
- Divide by a: x = -b/a
- 2x + 4 = 0
- 2x = -4
- x = -2
6. How are the zeroes of a polynomial related to its graph?
The zeroes of a polynomial are the x-coordinates where its graph intersects the x-axis. In graphical terms:
- If the graph cuts the x-axis at a point, that x-value is a zero.
- The number of zeroes equals the number of x-axis intersection points.
7. What is the difference between a monomial, binomial, and trinomial?
The difference between monomial, binomial, and trinomial is based on the number of terms. The classification is:
- Monomial: One term (Example: 5x²)
- Binomial: Two terms (Example: x + 3)
- Trinomial: Three terms (Example: x² + 2x + 1)
8. What is the value of a polynomial?
The value of a polynomial is the result obtained after substituting a given value of the variable into the polynomial. Steps:
- Replace the variable with the given number.
- Simplify using arithmetic operations.
- 2(2)² - 3(2) + 1
- 2(4) - 6 + 1
- 8 - 6 + 1 = 3
9. What is a constant polynomial?
A constant polynomial is a polynomial that has no variable and only a constant term. Its general form is p(x) = c, where c is a real number.
Example:
- 5
- -3
- 0
10. What are common mistakes to avoid in Polynomials MCQs for Class 9?
Common mistakes in Class 9 Polynomials MCQs include errors in identifying degree and zeroes. Important points to remember:
- Do not consider negative or fractional powers as polynomials.
- The degree is the highest exponent, not the number of terms.
- Check calculations carefully while substituting values.
- Remember that zero polynomial has no defined degree.
