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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn constant terms, coefficients, degree of polynomial, 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 that involve variables, coefficients, constants, and exponents. They are essential for understanding algebra and many advanced mathematical concepts. Learning polynomials helps students develop strong analytical and problem-solving skills.
What You Will Learn?
✔ Constant Terms
✔ Coefficients
✔ Degree of Polynomial
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Polynomial Classification
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are widely used in algebra and higher mathematics. Understanding their properties helps students solve equations, simplify expressions, and build a strong mathematical foundation.
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
$$5x^3-2x^2+7x-9$$
A)
$$5$$
B)
$$7$$
C)
$$-9$$
D)
$$3$$
Answer:
$$-9$$
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 in a polynomial.
Step-by-Step Solution:
Given polynomial:
$$5x^3-2x^2+7x-9$$
The term without
$$x$$
is:
$$-9$$
Therefore, the constant term is:
$$-9$$
Hence, the correct answer is:
$$-9$$
Exam Tip:
The constant term never contains a variable.
Q2. What is the degree of the polynomial
$$12x^7+3x^4-8x+2$$
A)
$$4$$
B)
$$5$$
C)
$$6$$
D)
$$7$$
Answer:
$$7$$
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 in the polynomial.
Step-by-Step Solution:
The powers of
$$x$$
are:
$$7,;4,;1,;0$$
The highest power is:
$$7$$
Therefore:
Degree
$$=7$$
Hence, the correct answer is:
$$7$$
Exam Tip:
Always look for the largest exponent, not the largest coefficient.
Q3. Find the value of
$$p(x)=x^2+5x+6$$
when
$$x=3$$
A)
$$28$$
B)
$$30$$
C)
$$32$$
D)
$$34$$
Answer:
$$30$$
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:
$$p(x)=x^2+5x+6$$
Substitute:
$$x=3$$
$$p(3)=3^2+5(3)+6$$
$$=9+15+6$$
$$=30$$
Therefore, the correct answer is:
$$30$$
Exam Tip:
Calculate powers before multiplication and addition.
Q4. Which of the following is a binomial?
A)
$$x^2+4x$$
B)
$$x^2+4x+5$$
C)
$$7x^2$$
D)
$$9$$
Answer:
$$x^2+4x$$
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:
$$x^2+4x$$
contains
$$2$$
terms.
$$x^2+4x+5$$
contains
$$3$$
terms.
$$7x^2$$
contains
$$1$$
term.
$$9$$
contains
$$1$$
term.
Therefore:
$$x^2+4x$$
is a binomial.
Hence, the correct answer is:
$$x^2+4x$$
Exam Tip:
Count the terms separated by plus or minus signs.
Q5. If
$$p(x)=x-20$$
then the zero of the polynomial is:
A)
$$20$$
B)
$$-20$$
C)
$$0$$
D)
$$2$$
Answer:
$$20$$
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:
$$p(x)=x-20$$
For zero:
$$x-20=0$$
$$x=20$$
Therefore:
The zero of the polynomial is
$$20$$
Hence, the correct answer is:
$$20$$
Exam Tip:
Set the polynomial equal to zero and solve carefully.
Important Formulas & Concepts
1. Constant Term
The term that does not contain any variable.
Example:
In
$$3x^2+4x+7$$
the constant term is:
$$7$$
2. Coefficient
The numerical factor attached to a variable.
Example:
In
$$8x^2$$
the coefficient is:
$$8$$
3. Degree of a Polynomial
The highest power of the variable present in the polynomial.
4. Binomial
A polynomial containing exactly two terms.
Example:
$$x+5$$
5. 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 without any variable.
2. What is a coefficient?
The numerical factor attached to a variable.
3. What is the degree of a polynomial?
The highest power of the variable present.
4. What is a binomial?
A polynomial having exactly two terms.
5. What is the zero of a polynomial?
The value that makes the polynomial equal to zero.
Common Mistakes
❌ Confusing the constant term with a coefficient.
❌ Ignoring the highest exponent while finding degree.
❌ Counting terms incorrectly.
❌ Making substitution mistakes.
❌ Forgetting sign changes while solving for zeros.
Quick Revision Notes
✔ Constant term → No variable.
✔ Coefficient → Numerical factor.
✔ Degree → Highest power of the variable.
✔ Binomial → Two terms.
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Substitute values carefully while evaluating.
Conclusion
Polynomials are a vital part of algebra and provide the foundation for many advanced mathematical concepts. Understanding constant terms, coefficients, degrees, values, and zeros of polynomials improves mathematical reasoning and problem-solving abilities. Regular MCQ practice helps students gain confidence and excel in examinations.
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