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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn degree of polynomial, constant polynomial, linear polynomial, quadratic 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 formed using variables, constants, and mathematical operations. They play a crucial role in algebra and are used extensively in higher mathematics. Understanding polynomials helps students solve equations and develop strong analytical skills.
What You Will Learn?
✔ Constant Polynomial
✔ Linear Polynomial
✔ Quadratic Polynomial
✔ Degree of Polynomial
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are the foundation of many mathematical concepts taught in higher classes. A clear understanding of polynomials helps students perform better in algebra and coordinate geometry.
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 constant polynomial?
A)
$$7$$
B)
$$x+5$$
C)
$$x^2+1$$
D)
$$2x^3$$
Answer:
$$7$$
Useful Formula for this Question:
A constant polynomial has degree:
$$0$$
Concept Behind This Question:
Students should identify a polynomial that does not contain any variable.
Step-by-Step Solution:
$$7$$
contains no variable.
Therefore, its degree is:
$$0$$
Hence, it is a constant polynomial.
Therefore, the correct answer is:
$$7$$
Exam Tip:
A constant polynomial contains only a numerical value.
Q2. What is the degree of the polynomial:
$$8x^3+4x^2-9x+1$$
A)
$$1$$
B)
$$2$$
C)
$$3$$
D)
$$4$$
Answer:
$$3$$
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:
Given polynomial:
$$8x^3+4x^2-9x+1$$
The powers of $$x$$ are:
$$3,;2,;1,;0$$
The highest power is:
$$3$$
Therefore:
Degree
$$=3$$
Hence, the correct answer is:
$$3$$
Exam Tip:
Always look for the term having the largest exponent.
Q3. Find the value of:
$$p(x)=x^2+4x+1$$
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 the polynomial correctly.
Step-by-Step Solution:
Given:
$$p(x)=x^2+4x+1$$
Substitute:
$$x=2$$
$$p(2)=2^2+4(2)+1$$
$$=4+8+1$$
$$=13$$
Therefore, the correct answer is:
$$13$$
Exam Tip:
Follow the BODMAS rule while simplifying.
Q4. Which of the following is a quadratic polynomial?
A)
$$4x+3$$
B)
$$x^2-7x+10$$
C)
$$5x^3+1$$
D)
$$12$$
Answer:
$$x^2-7x+10$$
Useful Formula for this Question:
A quadratic polynomial has degree:
$$2$$
Concept Behind This Question:
Students should identify a polynomial with highest power 2.
Step-by-Step Solution:
Degree of
$$4x+3$$
is
$$1$$
Degree of
$$x^2-7x+10$$
is
$$2$$
Degree of
$$5x^3+1$$
is
$$3$$
Degree of
$$12$$
is
$$0$$
Therefore:
$$x^2-7x+10$$
is a quadratic polynomial.
Hence, the correct answer is:
$$x^2-7x+10$$
Exam Tip:
Quadratic polynomials always have degree 2.
Q5. If
$$p(x)=x-9$$
then the zero of the polynomial is:
A)
$$9$$
B)
$$-9$$
C)
$$0$$
D)
$$1$$
Answer:
$$9$$
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 how to find zeros of linear polynomials.
Step-by-Step Solution:
Given:
$$p(x)=x-9$$
For zero:
$$x-9=0$$
$$x=9$$
Therefore:
The zero of the polynomial is
$$9$$
Hence, the correct answer is:
$$9$$
Exam Tip:
Set the polynomial equal to zero and solve for the variable.
Important Formulas & Concepts
1. Constant Polynomial
Degree:
$$0$$
Example:
$$5$$
2. Linear Polynomial
Degree:
$$1$$
Example:
$$2x+3$$
3. Quadratic Polynomial
Degree:
$$2$$
Example:
$$x^2+4x+1$$
4. Cubic Polynomial
Degree:
$$3$$
Example:
$$x^3+x+2$$
5. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a constant polynomial?
A polynomial that contains no variable.
2. What is the degree of a constant polynomial?
$$0$$
3. What is a quadratic polynomial?
A polynomial having degree
$$2$$
4. How do we find the value of a polynomial?
By substituting the given value of the variable.
5. What is a zero of a polynomial?
The value of the variable that makes the polynomial equal to zero.
Common Mistakes
❌ Confusing degree with coefficient.
❌ Ignoring the highest exponent.
❌ Substituting values incorrectly.
❌ Forgetting to simplify completely.
❌ Making sign errors while finding zeros.
Quick Revision Notes
✔ Constant polynomial → Degree
$$0$$
✔ Linear polynomial → Degree
$$1$$
✔ Quadratic polynomial → Degree
$$2$$
✔ Cubic polynomial → Degree
$$3$$
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Substitute values carefully while evaluating.
Conclusion
Polynomials are a fundamental topic in algebra and play an important role in higher mathematics. Understanding degrees, types of polynomials, values, and zeros helps students solve mathematical problems efficiently. Regular MCQ practice strengthens concepts and improves performance in examinations.
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