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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn degree of polynomial, coefficients, polynomial values, monomials, binomials, trinomials, and zeros of polynomials with detailed solutions for CBSE board exams.
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Chapter Information
Subject: Mathematics
Class: 9
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Polynomials are algebraic expressions formed by variables, coefficients, and constants. They are among the most important concepts in algebra and help students understand mathematical relationships, equations, and functions. Regular practice of polynomial questions improves logical thinking and problem-solving abilities.
What You Will Learn?
✔ Degree of Polynomial
✔ Coefficients and Constants
✔ Polynomial Values
✔ Monomials, Binomials and Trinomials
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Polynomial Classification
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials form the foundation for many higher-level mathematical concepts such as factorization, algebraic identities, and equations. A strong understanding of polynomials helps students solve problems more efficiently.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. What is the coefficient of
$$x^3$$
in the polynomial
$$18x^3-5x^2+4x-7$$
A)
$$18$$
B)
$$5$$
C)
$$4$$
D)
$$7$$
Answer:
$$18$$
Useful Formula for this Question:
The coefficient is the numerical factor attached to a variable term.
Concept Behind This Question:
Students should identify coefficients corresponding to a given power of a variable.
Step-by-Step Solution:
Given polynomial:
$$18x^3-5x^2+4x-7$$
The term containing
$$x^3$$
is:
$$18x^3$$
Therefore, the coefficient of
$$x^3$$
is:
$$18$$
Hence, the correct answer is:
$$18$$
Exam Tip:
Ignore the exponent and focus on the numerical factor.
Q2. Which of the following is a monomial?
A)
$$x^2+4x$$
B)
$$7x^5$$
C)
$$x+8$$
D)
$$x^2+2x+3$$
Answer:
$$7x^5$$
Useful Formula for this Question:
A monomial contains exactly one term.
Concept Behind This Question:
Students should classify algebraic expressions correctly.
Step-by-Step Solution:
$$x^2+4x$$
contains
$$2$$
terms.
$$7x^5$$
contains
$$1$$
term.
$$x+8$$
contains
$$2$$
terms.
$$x^2+2x+3$$
contains
$$3$$
terms.
Therefore:
$$7x^5$$
is a monomial.
Hence, the correct answer is:
$$7x^5$$
Exam Tip:
A monomial always contains only one term.
Q3. Find the value of
$$p(x)=5x^2-2x+1$$
when
$$x=3$$
A)
$$38$$
B)
$$40$$
C)
$$42$$
D)
$$44$$
Answer:
$$40$$
Useful Formula for this Question:
Substitute the given value of
$$x$$
into the polynomial.
Concept Behind This Question:
Students should evaluate polynomial expressions accurately.
Step-by-Step Solution:
Given:
$$p(x)=5x^2-2x+1$$
Substitute:
$$x=3$$
$$p(3)=5(3)^2-2(3)+1$$
$$=5(9)-6+1$$
$$=45-6+1$$
$$=40$$
Therefore, the correct answer is:
$$40$$
Exam Tip:
Follow BODMAS while simplifying expressions.
Q4. What is the degree of the polynomial
$$4x^{14}+8x^3-5$$
A)
$$3$$
B)
$$8$$
C)
$$14$$
D)
$$4$$
Answer:
$$14$$
Useful Formula for this Question:
The degree of a polynomial is the highest exponent of the variable.
Concept Behind This Question:
Students should identify the largest power present in the polynomial.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$14,;3,;0$$
The highest power is:
$$14$$
Therefore:
Degree
$$=14$$
Hence, the correct answer is:
$$14$$
Exam Tip:
The degree depends on the exponent, not the coefficient.
Q5. If
$$p(x)=x+28$$
then the zero of the polynomial is:
A)
$$28$$
B)
$$-28$$
C)
$$0$$
D)
$$2$$
Answer:
$$-28$$
Useful Formula for this Question:
A zero of a polynomial satisfies:
$$p(x)=0$$
Concept Behind This Question:
Students should determine the value that makes the polynomial equal to zero.
Step-by-Step Solution:
Given:
$$p(x)=x+28$$
For zero:
$$x+28=0$$
$$x=-28$$
Therefore:
The zero of the polynomial is
$$-28$$
Hence, the correct answer is:
$$-28$$
Exam Tip:
Set the polynomial equal to zero and solve carefully.
Important Formulas & Concepts
1. Coefficient
The numerical factor attached to a variable.
Example:
$$15x^2$$
Coefficient:
$$15$$
2. Constant Term
The term without a variable.
Example:
In
$$6x^2+4x+11$$
the constant term is:
$$11$$
3. Degree of a Polynomial
The highest exponent of the variable present in the polynomial.
4. Monomial, Binomial and Trinomial
Monomial:
$$8x^4$$
Binomial:
$$x+7$$
Trinomial:
$$x^2+4x+3$$
5. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a monomial?
A polynomial having exactly one term.
2. What is a coefficient?
The numerical factor attached to a variable.
3. What is the degree of a polynomial?
The highest exponent of the variable.
4. How do we evaluate a polynomial?
By substituting the value of the variable.
5. What is a zero of a polynomial?
The value that makes the polynomial equal to zero.
Common Mistakes
❌ Confusing coefficients with exponents.
❌ Counting terms incorrectly.
❌ Ignoring the highest power while finding degree.
❌ Making arithmetic mistakes during substitution.
❌ Forgetting negative signs while solving for zeros.
Quick Revision Notes
✔ Coefficient = Numerical factor.
✔ Constant term = No variable.
✔ Monomial = One term.
✔ Binomial = Two terms.
✔ Trinomial = Three terms.
✔ Degree = Highest exponent.
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Evaluate polynomials carefully using BODMAS.
Conclusion
Polynomials are one of the most important topics in Class 9 Mathematics. Understanding coefficients, constants, degrees, polynomial values, and zeros helps students develop strong algebraic skills and perform better in examinations. Regular MCQ practice improves confidence, speed, and accuracy.
Related Links
- Class9 Maths Chapter2 Polynomials part 10
- Class 9 Maths Chapter 2 Polynomials – Part 9
- Class 9 Maths Chapter 2 Polynomials degree of polynomial – Part 8
- Class 9 Maths Chapter 2 Polynomials – Part 7
- Class 9 Maths Chapter 2 Polynomials degree of polynomial – Part 6
- Class 9 Maths Chapter 2 Polynomials coefficients MCQ – Part 5
- Class 9 Maths Chapter 2 Polynomials, value of polynomials – Part 4
- Class 9 Maths Chapter 2 Polynomials constant polynomial – Part 3
- Class 9 Maths Chapter 2 Polynomials MCQ with solutuins – Part 2
- Class 9 Maths Chapter 1 Number Systems, irrational numbers
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