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Practice Class 9 Maths Chapter 2 Polynomials MCQ Questions with Answers based on NCERT syllabus. Learn monomials, binomials, trinomials, degree of polynomial, value of 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 important algebraic expressions that consist of variables and constants combined using mathematical operations. Understanding polynomials helps students solve algebraic problems, evaluate expressions, and build a strong foundation for higher mathematics.
What You Will Learn?
✔ Monomials
✔ Binomials
✔ Trinomials
✔ Degree of Polynomial
✔ Value of Polynomial
✔ Zeros of Polynomials
✔ Algebraic Expressions
✔ Board Exam Preparation
Why This Topic Is Important?
Polynomials are used extensively in algebra, coordinate geometry, and advanced mathematics. Learning this chapter 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. Which of the following is a monomial?
A)
$$x+5$$
B)
$$x^2+3x+1$$
C)
$$7x^3$$
D)
$$x^2-4$$
Answer:
$$7x^3$$
Useful Formula for this Question:
A monomial contains only one term.
Concept Behind This Question:
Students should identify algebraic expressions based on the number of terms.
Step-by-Step Solution:
$$x+5$$
has 2 terms.
$$x^2+3x+1$$
has 3 terms.
$$7x^3$$
has only 1 term.
$$x^2-4$$
has 2 terms.
Therefore:
$$7x^3$$
is a monomial.
Hence, the correct answer is:
$$7x^3$$
Exam Tip:
Count the number of terms before classifying the polynomial.
Q2. What is the degree of the polynomial:
$$9x^5-2x^2+7$$
A)
$$2$$
B)
$$3$$
C)
$$4$$
D)
$$5$$
Answer:
$$5$$
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:
$$9x^5-2x^2+7$$
The powers of $$x$$ are:
$$5,;2,;0$$
The highest power is:
$$5$$
Therefore:
Degree
$$=5$$
Hence, the correct answer is:
$$5$$
Exam Tip:
Do not add exponents; only identify the highest exponent.
Q3. Find the value of:
$$p(x)=3x^2+2$$
when
$$x=2$$
A)
$$10$$
B)
$$12$$
C)
$$14$$
D)
$$16$$
Answer:
$$14$$
Useful Formula for this Question:
Substitute the given value of $$x$$ into the polynomial.
Concept Behind This Question:
Students should evaluate the value of a polynomial correctly.
Step-by-Step Solution:
Given:
$$p(x)=3x^2+2$$
Substitute:
$$x=2$$
$$p(2)=3(2)^2+2$$
$$=3(4)+2$$
$$=12+2$$
$$=14$$
Therefore, the correct answer is:
$$14$$
Exam Tip:
Always solve powers before multiplication and addition.
Q4. Which of the following is a binomial?
A)
$$5x^2$$
B)
$$x^2+4x$$
C)
$$x^2+x+1$$
D)
$$9$$
Answer:
$$x^2+4x$$
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:
$$5x^2$$
has 1 term.
$$x^2+4x$$
has 2 terms.
$$x^2+x+1$$
has 3 terms.
$$9$$
has 1 term.
Therefore:
$$x^2+4x$$
is a binomial.
Hence, the correct answer is:
$$x^2+4x$$
Exam Tip:
A binomial always contains exactly two unlike terms.
Q5. If
$$p(x)=x+6$$
then the zero of the polynomial is:
A)
$$6$$
B)
$$-6$$
C)
$$0$$
D)
$$1$$
Answer:
$$-6$$
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 linear polynomial.
Step-by-Step Solution:
Given:
$$p(x)=x+6$$
For zero:
$$x+6=0$$
$$x=-6$$
Therefore:
The zero of the polynomial is
$$-6$$
Hence, the correct answer is:
$$-6$$
Exam Tip:
Put the polynomial equal to zero and solve for the variable.
Important Formulas & Concepts
1. Monomial
A polynomial having one term.
Example:
$$7x^2$$
2. Binomial
A polynomial having two terms.
Example:
$$x+5$$
3. Trinomial
A polynomial having three terms.
Example:
$$x^2+3x+2$$
4. Degree of a Polynomial
The highest power of the variable present in the polynomial.
5. Zero of a Polynomial
If
$$p(a)=0$$
then
$$a$$
is called a zero of the polynomial.
FAQs
1. What is a monomial?
A polynomial containing only one term.
2. What is a binomial?
A polynomial containing exactly two terms.
3. What is a trinomial?
A polynomial containing exactly three terms.
4. What is the degree of a polynomial?
The highest power of the variable present in the polynomial.
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.
❌ Counting terms incorrectly.
❌ Forgetting to substitute values properly.
❌ Making errors while solving for zeros.
❌ Ignoring powers while finding degree.
Quick Revision Notes
✔ Monomial → One term.
✔ Binomial → Two terms.
✔ Trinomial → Three terms.
✔ Degree = Highest power of the variable.
✔ Zero of polynomial means:
$$p(x)=0$$
✔ Substitute carefully while evaluating a polynomial.
Conclusion
Polynomials are an important part of algebra and help students understand mathematical expressions and equations. Learning monomials, binomials, trinomials, degrees, values, and zeros of polynomials builds a strong foundation for higher mathematics. Regular MCQ practice improves conceptual understanding and exam performance.
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