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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn coefficients, degree of polynomial, polynomial values, monomials, binomials, trinomials, 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 formed using variables, constants, coefficients, and exponents. They are one of the most important topics in algebra and help students understand equations, functions, and advanced mathematical concepts. Regular practice of polynomial-based questions strengthens problem-solving skills and mathematical reasoning.
What You Will Learn?
✔ Coefficients of Polynomials
✔ Degree of Polynomial
✔ Value of Polynomial
✔ Monomials, Binomials and Trinomials
✔ Constant Terms
✔ Zeros of Polynomials
✔ Polynomial Classification
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are widely used throughout mathematics. Understanding their properties helps students solve algebraic expressions efficiently and prepares them for higher-level concepts such as factorization and algebraic identities.
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
$$x^4$$
in the polynomial
$$11x^4-7x^2+5x-9$$
A)
$$4$$
B)
$$11$$
C)
$$7$$
D)
$$9$$
Answer:
$$11$$
Useful Formula for this Question:
The coefficient of a variable term is its numerical factor.
Concept Behind This Question:
Students should correctly identify coefficients associated with a given power of a variable.
Step-by-Step Solution:
Given polynomial:
$$11x^4-7x^2+5x-9$$
The term containing
$$x^4$$
is:
$$11x^4$$
Therefore, the coefficient of
$$x^4$$
is:
$$11$$
Hence, the correct answer is:
$$11$$
Exam Tip:
Look only at the numerical factor attached to the specified variable term.
Q2. Which of the following is a trinomial?
A)
$$9x^2$$
B)
$$x+4$$
C)
$$x^2+6x+8$$
D)
$$12$$
Answer:
$$x^2+6x+8$$
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:
$$9x^2$$
contains
$$1$$
term.
$$x+4$$
contains
$$2$$
terms.
$$x^2+6x+8$$
contains
$$3$$
terms.
$$12$$
contains
$$1$$
term.
Therefore:
$$x^2+6x+8$$
is a trinomial.
Hence, the correct answer is:
$$x^2+6x+8$$
Exam Tip:
Count each term separated by plus or minus signs.
Q3. Find the value of
$$p(x)=3x^2-2x+4$$
when
$$x=3$$
A)
$$25$$
B)
$$27$$
C)
$$29$$
D)
$$31$$
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 accurately.
Step-by-Step Solution:
Given:
$$p(x)=3x^2-2x+4$$
Substitute:
$$x=3$$
$$p(3)=3(3)^2-2(3)+4$$
$$=3(9)-6+4$$
$$=27-6+4$$
$$=25$$
Therefore, the correct answer is:
$$25$$
Exam Tip:
Follow BODMAS while evaluating polynomial values.
Q4. What is the degree of the polynomial
$$15x^{10}+4x^3-1$$
A)
$$3$$
B)
$$10$$
C)
$$15$$
D)
$$4$$
Answer:
$$10$$
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 in the polynomial.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$10,;3,;0$$
The highest power is:
$$10$$
Therefore:
Degree
$$=10$$
Hence, the correct answer is:
$$10$$
Exam Tip:
The degree depends only on the exponent, not on the coefficient.
Q5. If
$$p(x)=x+40$$
then the zero of the polynomial is:
A)
$$40$$
B)
$$-40$$
C)
$$0$$
D)
$$4$$
Answer:
$$-40$$
Useful Formula for this Question:
A zero of a polynomial is obtained by solving:
$$p(x)=0$$
Concept Behind This Question:
Students should understand how zeros of linear polynomials are calculated.
Step-by-Step Solution:
Given:
$$p(x)=x+40$$
For zero:
$$x+40=0$$
$$x=-40$$
Therefore:
The zero of the polynomial is
$$-40$$
Hence, the correct answer is:
$$-40$$
Exam Tip:
Replace the polynomial by zero and solve step-by-step.
Important Formulas & Concepts
1. Coefficient
The numerical factor multiplied by a variable.
Example:
In
$$8x^3$$
the coefficient is:
$$8$$
2. Constant Term
The term without a variable.
Example:
In
$$4x^2+3x+7$$
the constant term is:
$$7$$
3. Degree of a Polynomial
The highest exponent of the variable present in the polynomial.
4. Monomial, Binomial and Trinomial
Monomial:
$$5x^2$$
Binomial:
$$x+7$$
Trinomial:
$$x^2+3x+2$$
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 the degree of a polynomial?
The highest exponent of the variable present in the polynomial.
3. What is a trinomial?
A polynomial containing exactly three terms.
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 exponents.
❌ Counting polynomial terms incorrectly.
❌ Ignoring the highest power while finding degree.
❌ Making arithmetic mistakes during substitution.
❌ Forgetting negative 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 fundamental part of algebra and appear throughout mathematics. Understanding coefficients, terms, degrees, polynomial values, and zeros helps students build strong algebraic skills and perform well in examinations. Consistent MCQ practice improves conceptual clarity, speed, and accuracy.
Related Links
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