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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn polynomial values, coefficients, degree of polynomial, monomials, 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
Based On: NCERT Latest Syllabus
Introduction:
Polynomials are algebraic expressions formed using variables and constants. They help students understand algebraic relationships and develop problem-solving skills. Concepts such as degree, coefficient, value, and zero of a polynomial are frequently tested in school and board examinations.
What You Will Learn?
✔ Degree of Polynomial
✔ Coefficients
✔ Monomials, Binomials and Trinomials
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Polynomial Classification
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials form the basis of algebra and are used in various mathematical topics. Understanding them helps students solve equations and prepare for higher-level mathematics.
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
$$x$$
in the polynomial
$$4x^3+9x-5$$
A)
$$4$$
B)
$$9$$
C)
$$5$$
D)
$$3$$
Answer:
$$9$$
Useful Formula for this Question:
The coefficient of a variable is the numerical factor multiplied by that variable.
Concept Behind This Question:
Students should identify coefficients from different terms of a polynomial.
Step-by-Step Solution:
Given polynomial:
$$4x^3+9x-5$$
The term containing
$$x$$
is:
$$9x$$
Therefore, the coefficient of
$$x$$
is:
$$9$$
Hence, the correct answer is:
$$9$$
Exam Tip:
Look only at the term containing the specified variable power.
Q2. Which of the following is a monomial?
A)
$$x^2+3x$$
B)
$$5x^4$$
C)
$$x+7$$
D)
$$x^2+x+1$$
Answer:
$$5x^4$$
Useful Formula for this Question:
A monomial contains exactly one term.
Concept Behind This Question:
Students should classify polynomials based on the number of terms.
Step-by-Step Solution:
$$x^2+3x$$
contains
$$2$$
terms.
$$5x^4$$
contains
$$1$$
term.
$$x+7$$
contains
$$2$$
terms.
$$x^2+x+1$$
contains
$$3$$
terms.
Therefore:
$$5x^4$$
is a monomial.
Hence, the correct answer is:
$$5x^4$$
Exam Tip:
A monomial always consists of only one term.
Q3. Find the value of
$$p(x)=2x^2-3x+1$$
when
$$x=5$$
A)
$$36$$
B)
$$38$$
C)
$$40$$
D)
$$42$$
Answer:
$$36$$
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:
$$p(x)=2x^2-3x+1$$
Substitute:
$$x=5$$
$$p(5)=2(5)^2-3(5)+1$$
$$=2(25)-15+1$$
$$=50-15+1$$
$$=36$$
Therefore, the correct answer is:
$$36$$
Exam Tip:
Always solve exponents before multiplication.
Q4. What is the degree of the polynomial
$$10x^8+3x^2-6$$
A)
$$2$$
B)
$$6$$
C)
$$8$$
D)
$$10$$
Answer:
$$8$$
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 highest power correctly.
Step-by-Step Solution:
Given polynomial:
$$10x^8+3x^2-6$$
The powers of
$$x$$
are:
$$8,;2,;0$$
The highest power is:
$$8$$
Therefore:
Degree
$$=8$$
Hence, the correct answer is:
$$8$$
Exam Tip:
The coefficient does not affect the degree.
Q5. If
$$p(x)=x+25$$
then the zero of the polynomial is:
A)
$$25$$
B)
$$-25$$
C)
$$0$$
D)
$$5$$
Answer:
$$-25$$
Useful Formula for this Question:
A zero of a polynomial is the value of
$$x$$
for which:
$$p(x)=0$$
Concept Behind This Question:
Students should determine the value that makes the polynomial equal to zero.
Step-by-Step Solution:
Given:
$$p(x)=x+25$$
For zero:
$$x+25=0$$
$$x=-25$$
Therefore:
The zero of the polynomial is
$$-25$$
Hence, the correct answer is:
$$-25$$
Exam Tip:
Set the polynomial equal to zero before solving.
Important Formulas & Concepts
1. Monomial
A polynomial having one term.
Example:
$$7x^3$$
2. Binomial
A polynomial having two terms.
Example:
$$x+4$$
3. Trinomial
A polynomial having three terms.
Example:
$$x^2+3x+5$$
4. Degree of a Polynomial
The highest power of the variable present in the polynomial.
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 containing exactly one term.
2. What is a coefficient?
The numerical factor attached to a variable.
3. How do we find the degree of a polynomial?
By identifying the highest exponent of the variable.
4. What is the value of a polynomial?
The result obtained after substituting a value for 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 powers while finding degree.
❌ Making calculation mistakes during substitution.
❌ Forgetting negative signs while finding zeros.
Quick Revision Notes
✔ Monomial → One term.
✔ Binomial → Two terms.
✔ Trinomial → Three terms.
✔ Coefficient → Numerical factor.
✔ Degree → Highest power of the variable.
✔ Zero of polynomial means:
$$p(x)=0$$
Conclusion
Polynomials are a fundamental topic in algebra and are essential for understanding higher mathematics. Learning coefficients, degrees, polynomial values, and zeros helps students solve algebraic problems efficiently. Regular MCQ practice strengthens concepts and improves examination performance.
Related Links
- Class 9 Maths Chapter 2 Polynomials
- 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 2 Polynomials MCQ with solutions – Part 1
- Class 9 Maths Chapter 1 Number Systems laws of exponents
- 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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