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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn coefficients, polynomial values, degree of polynomial, algebraic expressions, 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 that involve variables, coefficients, constants, and exponents. They are a fundamental part of algebra and help students understand mathematical patterns, equations, and advanced problem-solving methods. Mastering polynomials is essential for success in higher mathematics.
What You Will Learn?
✔ Coefficients and Constants
✔ Degree of Polynomial
✔ Polynomial Values
✔ Monomials, Binomials and Trinomials
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Polynomial Classification
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are used extensively in algebra, coordinate geometry, and advanced mathematics. Understanding their properties helps students solve equations efficiently and develop logical reasoning skills.
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
$$x^2$$
in the polynomial
$$15x^4+9x^2-7x+3$$
A)
$$15$$
B)
$$9$$
C)
$$7$$
D)
$$3$$
Answer:
$$9$$
Useful Formula for this Question:
The coefficient of a variable term is the numerical factor attached to it.
Concept Behind This Question:
Students should correctly identify coefficients from polynomial expressions.
Step-by-Step Solution:
Given polynomial:
$$15x^4+9x^2-7x+3$$
The term containing
$$x^2$$
is:
$$9x^2$$
Therefore, the coefficient of
$$x^2$$
is:
$$9$$
Hence, the correct answer is:
$$9$$
Exam Tip:
Focus only on the term containing the required power of the variable.
Q2. Which of the following is a trinomial?
A)
$$8x^3$$
B)
$$x+6$$
C)
$$x^2+7x+10$$
D)
$$12$$
Answer:
$$x^2+7x+10$$
Useful Formula for this Question:
A trinomial contains exactly three terms.
Concept Behind This Question:
Students should classify polynomials based on the number of terms.
Step-by-Step Solution:
$$8x^3$$
contains
$$1$$
term.
$$x+6$$
contains
$$2$$
terms.
$$x^2+7x+10$$
contains
$$3$$
terms.
$$12$$
contains
$$1$$
term.
Therefore:
$$x^2+7x+10$$
is a trinomial.
Hence, the correct answer is:
$$x^2+7x+10$$
Exam Tip:
Count each separate term carefully.
Q3. Find the value of
$$p(x)=3x^2+4x+5$$
when
$$x=2$$
A)
$$21$$
B)
$$23$$
C)
$$25$$
D)
$$27$$
Answer:
$$25$$
Useful Formula for this Question:
Substitute the given value of
$$x$$
into the polynomial.
Concept Behind This Question:
Students should evaluate polynomial expressions correctly.
Step-by-Step Solution:
Given:
$$p(x)=3x^2+4x+5$$
Substitute:
$$x=2$$
$$p(2)=3(2)^2+4(2)+5$$
$$=3(4)+8+5$$
$$=12+8+5$$
$$=25$$
Therefore, the correct answer is:
$$25$$
Exam Tip:
Calculate powers first and then simplify.
Q4. What is the degree of the polynomial
$$9x^{13}+4x^6-2x+8$$
A)
$$6$$
B)
$$9$$
C)
$$13$$
D)
$$4$$
Answer:
$$13$$
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 exponent present.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$13,;6,;1,;0$$
The highest power is:
$$13$$
Therefore:
Degree
$$=13$$
Hence, the correct answer is:
$$13$$
Exam Tip:
The coefficient has no effect on the degree.
Q5. If
$$p(x)=x-35$$
then the zero of the polynomial is:
A)
$$35$$
B)
$$-35$$
C)
$$0$$
D)
$$5$$
Answer:
$$35$$
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:
$$p(x)=x-35$$
For zero:
$$x-35=0$$
$$x=35$$
Therefore:
The zero of the polynomial is
$$35$$
Hence, the correct answer is:
$$35$$
Exam Tip:
Set the polynomial equal to zero and solve step-by-step.
Important Formulas & Concepts
1. Coefficient
The numerical factor attached to a variable.
Example:
$$11x^2$$
Coefficient:
$$11$$
2. Constant Term
The term without a variable.
Example:
In
$$4x^2+3x+9$$
the constant term is:
$$9$$
3. Degree of a Polynomial
The highest exponent of the variable present in the polynomial.
4. Monomial, Binomial and Trinomial
Monomial:
$$7x^2$$
Binomial:
$$x+4$$
Trinomial:
$$x^2+5x+6$$
5. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a coefficient?
The numerical factor attached to a variable.
2. What is a trinomial?
A polynomial containing exactly three terms.
3. What is the degree of a polynomial?
The highest exponent of the variable present.
4. How do we find the value of a polynomial?
By substituting the given 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 substitution mistakes.
❌ Forgetting 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:
$$p(x)=0$$
Conclusion
Polynomials are a key topic in Class 9 Mathematics and provide the foundation for advanced algebraic concepts. Understanding coefficients, constants, degrees, polynomial values, and zeros helps students solve problems accurately and confidently. Regular MCQ practice strengthens concepts and improves examination performance.
Related Links
- 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
- Class 9 Maths Chapter 1 Number Systems, decimal expansion
- Class 9 Maths Chapter 1 Number Systems real numbers
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