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Practice Class 10 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn polynomials, degree of polynomial, types of polynomials, linear polynomial, quadratic polynomial, and cubic polynomial with detailed solutions and exam tips for CBSE board exams.
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Chapter Information
Subject: Mathematics
Class: 10
Chapter: Polynomials
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Easy
Based On: NCERT Latest Syllabus
Introduction:
Polynomials are one of the most important topics in algebra and form the foundation for many advanced mathematical concepts. In this chapter, students learn what polynomials are, how to identify their degree, and how to classify them as linear, quadratic, or cubic polynomials. Understanding polynomials is essential for solving equations, graph-related questions, and higher algebraic problems. Questions from this chapter are frequently asked in school examinations and board exams. This practice set contains beginner-friendly MCQs with detailed solutions and exam tips to help students build a strong foundation.
What You Will Learn?
✔ Meaning of Polynomial
✔ Degree of Polynomial
✔ Constant Polynomial
✔ Linear Polynomial
✔ Quadratic Polynomial
✔ Cubic Polynomial
✔ Board Exam Oriented Concepts
Why This Topic Is Important?
Polynomials are used throughout algebra and higher mathematics. A clear understanding of polynomial concepts helps students solve equations, understand graphs, and prepare for advanced topics in mathematics.
Exam Relevance
These questions are useful for:
✔ CBSE Board Exams
✔ State Board Exams
✔ School Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which of the following is a polynomial in $$x$$?
A) $$x+\frac{1}{x}$$
B) $$x^2+3x+2$$
C) $$\sqrt{x}+1$$
D) $$\frac{2}{x^2}+5$$
Answer:
$$x^2+3x+2$$
Useful Formula for this Question:
In a polynomial, the powers of the variable must be non-negative integers.
Concept Behind This Question:
A polynomial cannot contain variables in the denominator or variables with fractional powers.
Solution:
Option A contains:
$$\frac{1}{x}=x^{-1}$$
Option C contains:
$$\sqrt{x}=x^{\frac{1}{2}}$$
Option D contains:
$$\frac{2}{x^2}=2x^{-2}$$
Only:
$$x^2+3x+2$$
contains non-negative integer powers of $$x$$.
Therefore, the correct answer is:
$$x^2+3x+2$$
Exam Tip:
Whenever you see a variable in the denominator or under a square root, it is usually not a polynomial.
————————————————–
Q2. What is the degree of the polynomial:
$$5x^3+2x^2-7x+1$$
A) $$1$$
B) $$2$$
C) $$3$$
D) $$5$$
Answer:
$$3$$
Useful Formula for this Question:
Degree of a polynomial = Highest power of the variable.
Concept Behind This Question:
The degree helps classify a polynomial and determines many of its properties.
Solution:
The powers of $$x$$ are:
$$3,\ 2,\ 1,\ 0$$
The highest power is:
$$3$$
Therefore, the degree of the polynomial is:
$$3$$
Hence, the correct answer is:
$$3$$
Exam Tip:
Always look for the highest exponent of the variable, not the largest coefficient.
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Q3. Which of the following is a linear polynomial?
A) $$x^2+5$$
B) $$3x+7$$
C) $$x^3-1$$
D) $$x^4+2$$
Answer:
$$3x+7$$
Useful Formula for this Question:
A linear polynomial has degree:
$$1$$
Concept Behind This Question:
Polynomials are classified according to their degree.
Solution:
Degree of:
$$3x+7$$
is:
$$1$$
Therefore, it is a linear polynomial.
Hence, the correct answer is:
$$3x+7$$
Exam Tip:
Linear polynomial → Degree $$1$$
Quadratic polynomial → Degree $$2$$
Cubic polynomial → Degree $$3$$
————————————————–
Q4. Which of the following is a quadratic polynomial?
A) $$2x+1$$
B) $$x^3-4$$
C) $$x^2+5x+6$$
D) $$7$$
Answer:
$$x^2+5x+6$$
Useful Formula for this Question:
A quadratic polynomial has degree:
$$2$$
Concept Behind This Question:
Quadratic polynomials are among the most important types of polynomials and are widely used in algebra.
Solution:
The highest power of $$x$$ in:
$$x^2+5x+6$$
is:
$$2$$
Therefore, it is a quadratic polynomial.
Hence, the correct answer is:
$$x^2+5x+6$$
Exam Tip:
If the highest exponent is $$2$$, the polynomial is quadratic.
————————————————–
Q5. Which of the following is a constant polynomial?
A) $$4$$
B) $$x+4$$
C) $$x^2+1$$
D) $$x^3-2$$
Answer:
$$4$$
Useful Formula for this Question:
A constant polynomial contains no variable.
Concept Behind This Question:
Constant polynomials have degree $$0$$ and their value never changes.
Solution:
The expression:
$$4$$
contains no variable.
Therefore, it is a constant polynomial.
Hence, the correct answer is:
$$4$$
Exam Tip:
Any non-zero constant such as $$2$$, $$5$$, or $$100$$ is a constant polynomial.
————————————————–
Important Formulas and Concepts
Degree of Polynomial:
Highest power of the variable present in the polynomial.
Linear Polynomial:
Degree $$1$$
Quadratic Polynomial:
Degree $$2$$
Cubic Polynomial:
Degree $$3$$
Constant Polynomial:
Degree $$0$$
————————————————–
FAQs
Q. What is a polynomial?
Answer:
A polynomial is an algebraic expression in which the powers of the variable are non-negative integers.
Q. What is the degree of a polynomial?
Answer:
The highest power of the variable in the polynomial.
Q. What is a constant polynomial?
Answer:
A polynomial that contains no variable is called a constant polynomial.
————————————————–
Common Mistakes Students Make
❌ Confusing coefficients with degree.
❌ Considering $$\frac{1}{x}$$ as a polynomial term.
❌ Considering $$\sqrt{x}$$ as a polynomial term.
❌ Forgetting that a constant polynomial has degree $$0$$.
————————————————–
Quick Revision Notes
✔ A polynomial contains only non-negative integer powers of variables.
✔ Degree = Highest power of the variable.
✔ Linear polynomial → Degree $$1$$
✔ Quadratic polynomial → Degree $$2$$
✔ Cubic polynomial → Degree $$3$$
✔ Constant polynomial → Degree $$0$$
————————————————–
Conclusion:
These Class 10 Maths Chapter 2 Polynomials MCQs help students understand the basics of polynomials, degree of a polynomial, and types of polynomials. Mastering these concepts creates a strong foundation for solving algebraic equations and higher-level mathematics problems.
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