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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn polynomial classification, degree of polynomial, coefficients, value of polynomial, 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 consisting of variables, constants, coefficients, and exponents. They are used in various branches of mathematics and help students understand algebraic relationships and equations.
What You Will Learn?
✔ Polynomial Classification
✔ Coefficients
✔ Degree of Polynomial
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Monomials, Binomials and Trinomials
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are the foundation of algebra and are frequently used in higher mathematical concepts. Understanding them improves analytical thinking and problem-solving 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. Which of the following is a trinomial?
A)
$$7x^2$$
B)
$$x+9$$
C)
$$x^2+5x+6$$
D)
$$15$$
Answer:
$$x^2+5x+6$$
Useful Formula for this Question:
A trinomial contains exactly three terms.
Concept Behind This Question:
Students should classify polynomials according to the number of terms.
Step-by-Step Solution:
$$7x^2$$
contains
$$1$$
term.
$$x+9$$
contains
$$2$$
terms.
$$x^2+5x+6$$
contains
$$3$$
terms.
$$15$$
contains
$$1$$
term.
Therefore:
$$x^2+5x+6$$
is a trinomial.
Hence, the correct answer is:
$$x^2+5x+6$$
Exam Tip:
Count the terms carefully before classifying the polynomial.
Q2. What is the coefficient of
$$x^3$$
in
$$9x^3-4x+2$$
A)
$$3$$
B)
$$4$$
C)
$$9$$
D)
$$2$$
Answer:
$$9$$
Useful Formula for this Question:
The coefficient is the numerical factor attached to the variable.
Concept Behind This Question:
Students should identify coefficients correctly.
Step-by-Step Solution:
Given polynomial:
$$9x^3-4x+2$$
The term containing
$$x^3$$
is:
$$9x^3$$
Therefore, the coefficient of
$$x^3$$
is:
$$9$$
Hence, the correct answer is:
$$9$$
Exam Tip:
The coefficient is always the number multiplying the variable.
Q3. Find the value of
$$p(x)=2x^2+x+3$$
when
$$x=2$$
A)
$$11$$
B)
$$12$$
C)
$$13$$
D)
$$14$$
Answer:
$$13$$
Useful Formula for this Question:
Substitute the given value of
$$x$$
into the polynomial.
Concept Behind This Question:
Students should evaluate polynomial values correctly.
Step-by-Step Solution:
Given:
$$p(x)=2x^2+x+3$$
Substitute:
$$x=2$$
$$p(2)=2(2)^2+2+3$$
$$=2(4)+2+3$$
$$=8+2+3$$
$$=13$$
Therefore, the correct answer is:
$$13$$
Exam Tip:
Perform exponent operations before multiplication and addition.
Q4. What is the degree of the polynomial
$$4x^5+7x^2-3$$
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$5$$
Answer:
$$5$$
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 largest exponent present.
Step-by-Step Solution:
Given polynomial:
$$4x^5+7x^2-3$$
The powers of
$$x$$
are:
$$5,;2,;0$$
The highest power is:
$$5$$
Therefore:
Degree
$$=5$$
Hence, the correct answer is:
$$5$$
Exam Tip:
The coefficient does not affect the degree.
Q5. If
$$p(x)=x+15$$
then the zero of the polynomial is:
A)
$$15$$
B)
$$-15$$
C)
$$0$$
D)
$$1$$
Answer:
$$-15$$
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 understand the concept of zeros of polynomials.
Step-by-Step Solution:
Given:
$$p(x)=x+15$$
For zero:
$$x+15=0$$
$$x=-15$$
Therefore:
The zero of the polynomial is
$$-15$$
Hence, the correct answer is:
$$-15$$
Exam Tip:
Set the polynomial equal to zero and solve for the variable.
Important Formulas & Concepts
1. Monomial
A polynomial having one term.
Example:
$$8x^2$$
2. Binomial
A polynomial having two terms.
Example:
$$x+4$$
3. Trinomial
A polynomial having three terms.
Example:
$$x^2+5x+6$$
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 trinomial?
A polynomial containing exactly three terms.
2. What is a coefficient?
The numerical factor attached to a variable.
3. How is the degree of a polynomial found?
By identifying the highest power of the variable.
4. What is the zero of a polynomial?
The value that makes the polynomial equal to zero.
5. Can a polynomial have only one term?
Yes, it is called a monomial.
Common Mistakes
❌ Confusing coefficients with exponents.
❌ Counting terms incorrectly.
❌ Ignoring powers while finding degree.
❌ Making substitution errors.
❌ Forgetting sign changes while finding zeros.
Quick Revision Notes
✔ Monomial → One term.
✔ Binomial → Two terms.
✔ Trinomial → Three terms.
✔ Degree = Highest power of the variable.
✔ Coefficient = Numerical factor.
✔ Zero of polynomial means:
$$p(x)=0$$
Conclusion
Polynomials are one of the most important algebraic concepts in Class 9 Mathematics. Understanding coefficients, terms, degrees, values, and zeros of polynomials helps students build a strong mathematical foundation. Regular MCQ practice improves confidence, conceptual clarity, and exam performance.
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