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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn algebraic expressions, degree of polynomial, coefficients, zeros of polynomials, and value 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 important algebraic expressions consisting of variables, coefficients, and constants. They form the foundation of algebra and are widely used in mathematics. Understanding polynomials helps students simplify expressions, solve equations, and develop logical reasoning skills.
What You Will Learn?
✔ Algebraic Expressions
✔ Coefficients and Constants
✔ Degree of Polynomial
✔ Polynomial Classification
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Types of Polynomials
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are used throughout algebra and higher mathematics. A strong understanding of polynomial concepts helps students solve complex mathematical problems with confidence.
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
$$x^5$$
in the polynomial
$$14x^5-3x^2+8x-6$$
A)
$$14$$
B)
$$5$$
C)
$$3$$
D)
$$8$$
Answer:
$$14$$
Useful Formula for this Question:
The coefficient is the numerical factor multiplied by the variable.
Concept Behind This Question:
Students should identify the coefficient corresponding to a specific power of a variable.
Step-by-Step Solution:
Given polynomial:
$$14x^5-3x^2+8x-6$$
The term containing
$$x^5$$
is:
$$14x^5$$
Therefore, the coefficient of
$$x^5$$
is:
$$14$$
Hence, the correct answer is:
$$14$$
Exam Tip:
Ignore the exponent while identifying the coefficient.
Q2. Which of the following is a monomial?
A)
$$x^2+7$$
B)
$$x+9$$
C)
$$6x^4$$
D)
$$x^2+5x+1$$
Answer:
$$6x^4$$
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:
$$x^2+7$$
contains
$$2$$
terms.
$$x+9$$
contains
$$2$$
terms.
$$6x^4$$
contains
$$1$$
term.
$$x^2+5x+1$$
contains
$$3$$
terms.
Therefore:
$$6x^4$$
is a monomial.
Hence, the correct answer is:
$$6x^4$$
Exam Tip:
A monomial always has only one term.
Q3. Find the value of
$$p(x)=4x^2+x-2$$
when
$$x=2$$
A)
$$14$$
B)
$$16$$
C)
$$18$$
D)
$$20$$
Answer:
$$16$$
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:
$$p(x)=4x^2+x-2$$
Substitute:
$$x=2$$
$$p(2)=4(2)^2+2-2$$
$$=4(4)+2-2$$
$$=16$$
Therefore, the correct answer is:
$$16$$
Exam Tip:
Always calculate powers before multiplication.
Q4. What is the degree of the polynomial
$$7x^{11}+2x^4-9$$
A)
$$4$$
B)
$$7$$
C)
$$9$$
D)
$$11$$
Answer:
$$11$$
Useful Formula for this Question:
The degree of a polynomial is the highest power of the variable.
Concept Behind This Question:
Students should identify the highest exponent present.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$11,;4,;0$$
The highest power is:
$$11$$
Therefore:
Degree
$$=11$$
Hence, the correct answer is:
$$11$$
Exam Tip:
The coefficient does not affect the degree.
Q5. If
$$p(x)=x-18$$
then the zero of the polynomial is:
A)
$$18$$
B)
$$-18$$
C)
$$0$$
D)
$$1$$
Answer:
$$18$$
Useful Formula for this Question:
A zero of a polynomial satisfies:
$$p(x)=0$$
Concept Behind This Question:
Students should understand how to determine zeros of linear polynomials.
Step-by-Step Solution:
Given:
$$p(x)=x-18$$
For zero:
$$x-18=0$$
$$x=18$$
Therefore:
The zero of the polynomial is
$$18$$
Hence, the correct answer is:
$$18$$
Exam Tip:
Set the polynomial equal to zero and solve carefully.
Important Formulas & Concepts
1. Coefficient
The numerical factor attached to a variable.
Example:
$$12x^2$$
Coefficient:
$$12$$
2. Constant Term
The term without any variable.
Example:
In
$$5x^2+3x+8$$
Constant Term:
$$8$$
3. Degree of a Polynomial
The highest power of the variable present in the polynomial.
4. Monomial, Binomial and Trinomial
Monomial:
$$7x^3$$
Binomial:
$$x+8$$
Trinomial:
$$x^2+5x+4$$
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. 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 and exponents.
❌ Counting terms incorrectly.
❌ Ignoring the highest power while finding degree.
❌ Making mistakes during substitution.
❌ Forgetting negative signs while solving equations.
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 an essential part of algebra and provide the foundation for advanced mathematical concepts. Understanding coefficients, constants, degrees, polynomial values, and zeros helps students improve their problem-solving skills and examination performance. Regular MCQ practice strengthens concepts and builds confidence.
Related Links
- Class 9 Maths Chapter 2 Polynomials
- Class 9 Maths Chapter 2 Polynomials degree of polynomial
- Class 9 Maths Chapter 2 Polynomials 2
- 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 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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