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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn degree of polynomial, coefficients, constant terms, polynomial values, 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 made up of variables, coefficients, constants, and exponents. They form the basis of algebra and help students understand mathematical relationships, equations, and advanced problem-solving techniques.
What You Will Learn?
✔ Degree of Polynomial
✔ Coefficients
✔ Constant Terms
✔ Polynomial Values
✔ Zeros of Polynomials
✔ Types of Polynomials
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are widely used in algebra, coordinate geometry, and higher mathematics. Understanding their properties helps students solve mathematical problems efficiently and prepares them for advanced topics.
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 constant term in the polynomial
$$9x^5-4x^2+7x+15$$
A)
$$9$$
B)
$$7$$
C)
$$15$$
D)
$$5$$
Answer:
$$15$$
Useful Formula for this Question:
The constant term is the term that does not contain any variable.
Concept Behind This Question:
Students should identify the constant term correctly.
Step-by-Step Solution:
Given polynomial:
$$9x^5-4x^2+7x+15$$
The term without
$$x$$
is:
$$15$$
Therefore, the constant term is:
$$15$$
Hence, the correct answer is:
$$15$$
Exam Tip:
The constant term remains unchanged for every value of the variable.
Q2. Which of the following is a binomial?
A)
$$8x^2+5$$
B)
$$x^2+4x+7$$
C)
$$9x^3$$
D)
$$12$$
Answer:
$$8x^2+5$$
Useful Formula for this Question:
A binomial contains exactly two terms.
Concept Behind This Question:
Students should classify polynomials according to the number of terms.
Step-by-Step Solution:
$$8x^2+5$$
contains
$$2$$
terms.
$$x^2+4x+7$$
contains
$$3$$
terms.
$$9x^3$$
contains
$$1$$
term.
$$12$$
contains
$$1$$
term.
Therefore:
$$8x^2+5$$
is a binomial.
Hence, the correct answer is:
$$8x^2+5$$
Exam Tip:
Count terms separated by plus or minus signs.
Q3. Find the value of
$$p(x)=2x^2+5x+3$$
when
$$x=4$$
A)
$$45$$
B)
$$50$$
C)
$$55$$
D)
$$60$$
Answer:
$$55$$
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:
$$p(x)=2x^2+5x+3$$
Substitute:
$$x=4$$
$$p(4)=2(4)^2+5(4)+3$$
$$=2(16)+20+3$$
$$=32+20+3$$
$$=55$$
Therefore, the correct answer is:
$$55$$
Exam Tip:
Apply BODMAS while simplifying polynomial values.
Q4. What is the degree of the polynomial
$$5x^{12}+7x^4-3x+1$$
A)
$$4$$
B)
$$7$$
C)
$$12$$
D)
$$5$$
Answer:
$$12$$
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.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$12,;4,;1,;0$$
The highest power is:
$$12$$
Therefore:
Degree
$$=12$$
Hence, the correct answer is:
$$12$$
Exam Tip:
The coefficient does not affect the degree.
Q5. If
$$p(x)=x+22$$
then the zero of the polynomial is:
A)
$$22$$
B)
$$-22$$
C)
$$0$$
D)
$$2$$
Answer:
$$-22$$
Useful Formula for this Question:
A zero of a polynomial satisfies:
$$p(x)=0$$
Concept Behind This Question:
Students should determine the value of
$$x$$
that makes the polynomial equal to zero.
Step-by-Step Solution:
Given:
$$p(x)=x+22$$
For zero:
$$x+22=0$$
$$x=-22$$
Therefore:
The zero of the polynomial is
$$-22$$
Hence, the correct answer is:
$$-22$$
Exam Tip:
Set the polynomial equal to zero and solve carefully.
Important Formulas & Concepts
1. Constant Term
The term without any variable.
Example:
In
$$6x^2+5x+11$$
the constant term is:
$$11$$
2. Coefficient
The numerical factor attached to a variable.
Example:
In
$$13x^3$$
the coefficient is:
$$13$$
3. Degree of a Polynomial
The highest exponent of the variable present in the polynomial.
4. Binomial
A polynomial having exactly two terms.
Example:
$$x+9$$
5. Trinomial
A polynomial having exactly three terms.
Example:
$$x^2+3x+4$$
6. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a constant term?
A term that does not contain any variable.
2. What is a binomial?
A polynomial containing exactly two terms.
3. What is the degree of a polynomial?
The highest exponent of the variable.
4. How do we evaluate 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 constants.
❌ Ignoring the highest exponent while finding degree.
❌ Counting terms incorrectly.
❌ Making arithmetic mistakes during substitution.
❌ Forgetting sign changes while finding zeros.
Quick Revision Notes
✔ Constant term → No variable.
✔ Coefficient → Numerical factor.
✔ Binomial → Two terms.
✔ Trinomial → Three terms.
✔ Degree → Highest exponent.
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Substitute values carefully before simplification.
Conclusion
Polynomials are among the most important topics in Class 9 Mathematics. A strong understanding of coefficients, constants, degrees, values, and zeros of polynomials helps students solve algebraic problems confidently. Regular MCQ practice improves conceptual clarity, accuracy, and examination performance.
Related Links
- Class 9 Maths Chapter 2 Polynomials degree of polynomial
- Class 9 Maths Chapter 2 Polynomials
- Class 9 Maths Chapter 2 Polynomials degree of polynomial
- Class 9 Maths Chapter 2 Polynomials coefficients MCQ
- 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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