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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn cubic polynomials, degree of polynomial, value of polynomials, zeros of polynomials, and algebraic expressions 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 consisting of variables, constants, and exponents. They are used extensively in algebra and form the basis for many advanced mathematical concepts. Understanding polynomials helps students solve equations and improve logical reasoning skills.
What You Will Learn?
✔ Cubic Polynomials
✔ Degree of Polynomial
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Types of Polynomials
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are used in algebra, coordinate geometry, and higher mathematics. Learning this chapter strengthens problem-solving abilities and develops a deeper understanding of mathematical relationships.
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 cubic polynomial?
A)
$$x+4$$
B)
$$x^2+3$$
C)
$$2x^3-5x+1$$
D)
$$7$$
Answer:
$$2x^3-5x+1$$
Useful Formula for this Question:
A cubic polynomial has degree:
$$3$$
Concept Behind This Question:
Students should identify polynomials based on their degree.
Step-by-Step Solution:
Degree of
$$x+4$$
is
$$1$$
Degree of
$$x^2+3$$
is
$$2$$
Degree of
$$2x^3-5x+1$$
is
$$3$$
Degree of
$$7$$
is
$$0$$
Therefore:
$$2x^3-5x+1$$
is a cubic polynomial.
Hence, the correct answer is:
$$2x^3-5x+1$$
Exam Tip:
A cubic polynomial always has highest power
$$3$$
Q2. What is the degree of the polynomial:
$$6x^4-3x^2+8$$
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$6$$
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 largest exponent in the polynomial.
Step-by-Step Solution:
Given polynomial:
$$6x^4-3x^2+8$$
The powers of $$x$$ are:
$$4,;2,;0$$
The highest power is:
$$4$$
Therefore:
Degree
$$=4$$
Hence, the correct answer is:
$$4$$
Exam Tip:
Ignore coefficients while finding the degree.
Q3. Find the value of:
$$p(x)=2x^2+3x+4$$
when
$$x=1$$
A)
$$7$$
B)
$$8$$
C)
$$9$$
D)
$$10$$
Answer:
$$9$$
Useful Formula for this Question:
Substitute the given value of $$x$$ into the polynomial.
Concept Behind This Question:
Students should evaluate a polynomial accurately.
Step-by-Step Solution:
Given:
$$p(x)=2x^2+3x+4$$
Substitute:
$$x=1$$
$$p(1)=2(1)^2+3(1)+4$$
$$=2+3+4$$
$$=9$$
Therefore, the correct answer is:
$$9$$
Exam Tip:
Substitute carefully and simplify step by step.
Q4. Which of the following is a trinomial?
A)
$$5x^2$$
B)
$$x+7$$
C)
$$x^2+4x+6$$
D)
$$12$$
Answer:
$$x^2+4x+6$$
Useful Formula for this Question:
A trinomial contains exactly three terms.
Concept Behind This Question:
Students should classify polynomials based on the number of terms.
Step-by-Step Solution:
$$5x^2$$
has
$$1$$
term.
$$x+7$$
has
$$2$$
terms.
$$x^2+4x+6$$
has
$$3$$
terms.
$$12$$
has
$$1$$
term.
Therefore:
$$x^2+4x+6$$
is a trinomial.
Hence, the correct answer is:
$$x^2+4x+6$$
Exam Tip:
Count the terms separated by plus or minus signs.
Q5. If
$$p(x)=x+8$$
then the zero of the polynomial is:
A)
$$8$$
B)
$$-8$$
C)
$$0$$
D)
$$1$$
Answer:
$$-8$$
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 the zero of a polynomial.
Step-by-Step Solution:
Given:
$$p(x)=x+8$$
For zero:
$$x+8=0$$
$$x=-8$$
Therefore:
The zero of the polynomial is
$$-8$$
Hence, the correct answer is:
$$-8$$
Exam Tip:
Set the polynomial equal to zero and solve for the variable.
Important Formulas & Concepts
1. Constant Polynomial
Degree:
$$0$$
Example:
$$9$$
2. Linear Polynomial
Degree:
$$1$$
Example:
$$3x+4$$
3. Quadratic Polynomial
Degree:
$$2$$
Example:
$$x^2+5x+2$$
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 cubic polynomial?
A polynomial having degree
$$3$$
2. What is a trinomial?
A polynomial having exactly three terms.
3. How is the degree of a polynomial determined?
By identifying the highest power of the variable.
4. What is a zero of a polynomial?
The value of the variable that makes the polynomial equal to zero.
5. Can a constant polynomial have a variable?
No, a constant polynomial contains no variable.
Common Mistakes
❌ Confusing the number of terms with degree.
❌ Ignoring the highest exponent.
❌ Making substitution errors.
❌ Forgetting to set the polynomial equal to zero.
❌ Counting terms incorrectly.
Quick Revision Notes
✔ Constant polynomial → Degree
$$0$$
✔ Linear polynomial → Degree
$$1$$
✔ Quadratic polynomial → Degree
$$2$$
✔ Cubic polynomial → Degree
$$3$$
✔ Trinomial → Three terms.
✔ Zero of polynomial means:
$$p(x)=0$$
Conclusion
Polynomials are a key part of algebra and are widely used in mathematics. Understanding the degree, types, values, and zeros of polynomials helps students develop strong problem-solving skills and perform well in examinations. Regular practice of MCQs improves accuracy and conceptual understanding.
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