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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn polynomial classification, degree of polynomial, coefficients, constant terms, 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 consist of variables, coefficients, and constants. They are an important part of algebra and help students understand mathematical relationships, equations, and advanced concepts in higher classes.
What You Will Learn?
✔ Constant Terms
✔ Coefficients
✔ Degree of Polynomial
✔ Polynomial Classification
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are widely used in algebra and many other branches of mathematics. Understanding their properties helps students solve mathematical problems more efficiently and accurately.
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
$$8x^4+5x^2-3x+12$$
A)
$$8$$
B)
$$5$$
C)
$$12$$
D)
$$3$$
Answer:
$$12$$
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 correctly.
Step-by-Step Solution:
Given polynomial:
$$8x^4+5x^2-3x+12$$
The term without
$$x$$
is:
$$12$$
Therefore, the constant term is:
$$12$$
Hence, the correct answer is:
$$12$$
Exam Tip:
The constant term remains unchanged regardless of the value of the variable.
Q2. Which of the following is a binomial?
A)
$$4x^2+7$$
B)
$$x^2+x+1$$
C)
$$9x^3$$
D)
$$15$$
Answer:
$$4x^2+7$$
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:
$$4x^2+7$$
contains
$$2$$
terms.
$$x^2+x+1$$
contains
$$3$$
terms.
$$9x^3$$
contains
$$1$$
term.
$$15$$
contains
$$1$$
term.
Therefore:
$$4x^2+7$$
is a binomial.
Hence, the correct answer is:
$$4x^2+7$$
Exam Tip:
Count terms separated by plus or minus signs.
Q3. Find the value of
$$p(x)=x^2+2x+7$$
when
$$x=4$$
A)
$$29$$
B)
$$30$$
C)
$$31$$
D)
$$32$$
Answer:
$$31$$
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:
$$p(x)=x^2+2x+7$$
Substitute:
$$x=4$$
$$p(4)=4^2+2(4)+7$$
$$=16+8+7$$
$$=31$$
Therefore, the correct answer is:
$$31$$
Exam Tip:
Perform exponent calculations first, then multiplication and addition.
Q4. What is the degree of the polynomial
$$13x^9+5x^4-2$$
A)
$$4$$
B)
$$5$$
C)
$$9$$
D)
$$13$$
Answer:
$$9$$
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 correctly.
Step-by-Step Solution:
Given polynomial:
$$13x^9+5x^4-2$$
The powers of
$$x$$
are:
$$9,;4,;0$$
The highest power is:
$$9$$
Therefore:
Degree
$$=9$$
Hence, the correct answer is:
$$9$$
Exam Tip:
Ignore coefficients while finding the degree.
Q5. If
$$p(x)=x-30$$
then the zero of the polynomial is:
A)
$$30$$
B)
$$-30$$
C)
$$0$$
D)
$$3$$
Answer:
$$30$$
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:
$$p(x)=x-30$$
For zero:
$$x-30=0$$
$$x=30$$
Therefore:
The zero of the polynomial is
$$30$$
Hence, the correct answer is:
$$30$$
Exam Tip:
Set the polynomial equal to zero and solve for the variable.
Important Formulas & Concepts
1. Constant Term
The term that does not contain any variable.
Example:
In
$$5x^2+3x+8$$
the constant term is:
$$8$$
2. Monomial
A polynomial having one term.
Example:
$$7x^4$$
3. Binomial
A polynomial having two terms.
Example:
$$x^2+5$$
4. Trinomial
A polynomial having three terms.
Example:
$$x^2+3x+2$$
5. Degree of a Polynomial
The highest power of the variable present in the polynomial.
6. 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 that does not contain any variable.
2. What is a binomial?
A polynomial containing exactly two terms.
3. What is the degree of a polynomial?
The highest power of the variable present in the polynomial.
4. How do we evaluate a polynomial?
By substituting the given value of the variable.
5. What is a zero of a polynomial?
The value that makes the polynomial equal to zero.
Common Mistakes
❌ Confusing constant terms with coefficients.
❌ Counting terms incorrectly.
❌ Ignoring the highest exponent.
❌ Making arithmetic mistakes during substitution.
❌ Forgetting sign changes while solving for zeros.
Quick Revision Notes
✔ Constant term → No variable.
✔ Monomial → One term.
✔ Binomial → Two terms.
✔ Trinomial → Three terms.
✔ Degree → Highest power of the variable.
✔ Zero of polynomial means:
$$p(x)=0$$
Conclusion
Polynomials are a crucial part of algebra and help students understand mathematical expressions and equations. A strong understanding of coefficients, terms, degrees, values, and zeros of polynomials improves problem-solving skills and builds confidence for examinations. Regular MCQ practice strengthens conceptual understanding and accuracy.
Related Links
- Class 9 Maths Chapter 2 Polynomials 2
- Class 9 Maths Chapter 2 Polynomials
- Class 9 Maths Chapter 2 Polynomials coefficients MCQ
- Class 9 Maths Chapter 2 Polynomials, value of polynomials – Part 4
- Class 9 Maths Chapter 2 Polynomials constant polynomial – Part 3
- Class 9 Maths Chapter 2 Polynomials MCQ with solutuins – Part 2
- 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
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