Welcome To My School Study
Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn degree of polynomial, types of polynomials, zeros of polynomials, value of polynomial, and algebraic expressions with detailed solutions for CBSE board exams.
Do You Know
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 one of the most important topics in algebra. In this chapter, students learn about algebraic expressions, terms, coefficients, variables, degrees of polynomials, and zeros of polynomials. Understanding polynomials helps students solve algebraic equations and prepares them for higher-level mathematics.
What You Will Learn?
✔ Algebraic Expressions
✔ Terms and Coefficients
✔ Degree of Polynomial
✔ Types of Polynomials
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Graphical Representation of Polynomials
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials form the foundation of algebra. The concepts learned in this chapter are used in equations, coordinate geometry, quadratic equations, and higher mathematics. A strong understanding of polynomials improves logical 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. What is the degree of the polynomial:
$$5x^4 + 2x^2 – 7$$
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$5$$
Answer:
$$4$$
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 in the polynomial.
Step-by-Step Solution:
Given polynomial:
$$5x^4 + 2x^2 – 7$$
The powers of $$x$$ are:
$$4,;2,;0$$
The highest power is:
$$4$$
Therefore:
Degree
$$= 4$$
Hence, the correct answer is:
$$4$$
Exam Tip:
Always look for the highest exponent of the variable.
Q2. Which of the following is a linear polynomial?
A)
$$x^2 + 5$$
B)
$$3x + 2$$
C)
$$x^3 – 1$$
D)
$$5x^4 + 7$$
Answer:
$$3x + 2$$
Useful Formula for this Question:
A linear polynomial has degree:
$$1$$
Concept Behind This Question:
Students should classify polynomials according to their degrees.
Step-by-Step Solution:
Degree of
$$x^2 + 5$$
is
$$2$$
Degree of
$$3x + 2$$
is
$$1$$
Degree of
$$x^3 – 1$$
is
$$3$$
Degree of
$$5x^4 + 7$$
is
$$4$$
Only
$$3x + 2$$
has degree
$$1$$
Therefore, the correct answer is:
$$3x + 2$$
Exam Tip:
A polynomial with highest power 1 is called a linear polynomial.
Q3. Find the value of:
$$p(x)=2x+5$$
when
$$x=3$$
A)
$$9$$
B)
$$10$$
C)
$$11$$
D)
$$12$$
Answer:
$$11$$
Useful Formula for this Question:
Substitute the given value of $$x$$ into the polynomial.
Concept Behind This Question:
Students should evaluate a polynomial for a given value.
Step-by-Step Solution:
Given:
$$p(x)=2x+5$$
Substitute:
$$x=3$$
$$p(3)=2(3)+5$$
$$=6+5$$
$$=11$$
Therefore, the correct answer is:
$$11$$
Exam Tip:
Replace the variable carefully before simplifying.
Q4. Which of the following is a quadratic polynomial?
A)
$$x+7$$
B)
$$x^2+3x+1$$
C)
$$x^3+2$$
D)
$$5$$
Answer:
$$x^2+3x+1$$
Useful Formula for this Question:
A quadratic polynomial has degree:
$$2$$
Concept Behind This Question:
Students should identify polynomials based on degree.
Step-by-Step Solution:
Degree of
$$x+7$$
is
$$1$$
Degree of
$$x^2+3x+1$$
is
$$2$$
Degree of
$$x^3+2$$
is
$$3$$
Degree of
$$5$$
is
$$0$$
Therefore,
$$x^2+3x+1$$
is a quadratic polynomial.
Hence, the correct answer is:
$$x^2+3x+1$$
Exam Tip:
Quadratic means the highest power of the variable is 2.
Q5. If
$$p(x)=x-4$$
then the zero of the polynomial is:
A)
$$0$$
B)
$$2$$
C)
$$4$$
D)
$$-4$$
Answer:
$$4$$
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 meaning of a polynomial’s zero.
Step-by-Step Solution:
Given:
$$p(x)=x-4$$
For zero:
$$x-4=0$$
$$x=4$$
Therefore:
The zero of the polynomial is
$$4$$
Hence, the correct answer is:
$$4$$
Exam Tip:
Put the polynomial equal to zero and solve for the variable.
Important Formulas & Concepts
1. Degree of a Polynomial
The highest power of the variable is called the degree of the polynomial.
2. Linear Polynomial
Degree:
$$1$$
Example:
$$2x+3$$
3. Quadratic Polynomial
Degree:
$$2$$
Example:
$$x^2+5x+6$$
4. Cubic Polynomial
Degree:
$$3$$
Example:
$$x^3+2x+1$$
5. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a polynomial?
A polynomial is an algebraic expression consisting of variables and constants connected by addition, subtraction, and multiplication.
2. What is the degree of a polynomial?
The highest power of the variable present in the polynomial.
3. What is a linear polynomial?
A polynomial having degree
$$1$$
4. What is a quadratic polynomial?
A polynomial having degree
$$2$$
5. What is a zero of a polynomial?
The value of the variable that makes the polynomial equal to zero.
Common Mistakes
❌ Confusing coefficient with degree.
❌ Taking the number of terms as the degree.
❌ Forgetting to substitute values correctly.
❌ Incorrectly identifying polynomial zeros.
❌ Ignoring the highest exponent while finding degree.
Quick Revision Notes
✔ Degree = Highest power of the variable.
✔ Linear polynomial → Degree
$$1$$
✔ Quadratic polynomial → Degree
$$2$$
✔ Cubic polynomial → Degree
$$3$$
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Substitute carefully while finding the value of a polynomial.
Conclusion
Polynomials are a fundamental part of algebra and form the basis for many advanced mathematical concepts. Understanding degrees, types of polynomials, values, and zeros helps students solve algebraic problems efficiently and prepares them for higher-level mathematics. Regular MCQ practice strengthens conceptual understanding and improves exam performance.
Related Links
- Quiz Class 9th Science past 1
- Class 9 Maths – Number Systems, real numbers
- Class 9 Maths- Number Systems
- Class 9 Maths Chapter 1 Number Systems laws of exponents
- 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
- Class 9 Maths Chapter 1 Number Systems decimal expansion
- Class 9 Maths Chapter 1 Number Systems
Latest Posts
- Class 7 Maths Chapter 3 Data Handling
- Class 9 Maths Chapter 3 Coordinate Geometry
- Class 10 Maths Chapter 3 Pair of Linear Equations in Two
- Class 8 Maths Chapter 3 Understanding Quadrilaterals
- Class 7 Maths Chapter 3 Data Handling, data collection
Join Our Other Communities
Instagram , Youtube , Facebook
