Polynomials Class 9 Important Questions Free PDF Download

Polynomials form a vital part of Class 9 CBSE Maths and serve as the foundation for many advanced algebraic concepts. To score well in exams, understanding the key concepts of polynomials isn’t enough—you also need to practice solving a variety of questions. From finding zeroes and factorizing polynomials to applying the Remainder and Factor Theorems, this chapter offers plenty of opportunities to boost your problem-solving skills.

In this blog, we’ve compiled a list of the most important questions from Chapter 2: Polynomials to help you prepare effectively. Covering all the crucial topics, these questions are designed to strengthen your conceptual knowledge and enhance your confidence for exams. Whether you’re revising for your board exams or brushing up on your algebra skills, practising these Polynomials Class 9 Important Questions will ensure you’re well-prepared to tackle any polynomial problem that comes your way!

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Chapter 2 Polynomials Class 9: Important Questions

1. The number of zeros of the polynomial x²+ 4x + 2 is/are:

a. 1                                                       b. 2

c. 3                                                       d. 4

Solution: 

(b) 2

Explanation:

To determine the number of zeros of the polynomial x²+ 4x + 2, we analyze its degree. The degree of a polynomial is the highest power of x in the expression. For x²+ 4x + 2, the highest power of x is 2. Therefore, the polynomial is of degree 2. A polynomial of degree n has exactly n zeros (real or complex). Since this is a quadratic polynomial (n=2), it has 2 zeros.

2. Assertion: If x=1 is zero of polynomial 2x²+kx-12, then k =10

Reason: If x=a is zero of polynomial f(x), then f(-a) =0.

a. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion                                                   

b. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c. Assertion is true but the reason is false.

d. Both assertion and reason are false.

Solution:

‍(c) Assertion is true but the reason is false.

‍Explanation:

‍Assertion:

"If x=1 is a zero of the polynomial 2x²+kx−12, then k=10.

"If x=1 is a zero of the polynomial, then substituting x=1 into f(x)=2x²+kx−12 should make f(x)=0

f(1)= 2(1)²+k(1)−12

=2+k−12

k=10

Thus, the assertion is true.

‍Reason:

‍"If x=a is a zero of the polynomial f(x), then f(−a)=0."This statement is false.

If x=a is a zero of f(x), it means f(a)=0.

There is no general relationship that f(−a)=0 unless the polynomial has specific symmetry (e.g., all odd-power terms cancel out).

3. If (x+2) is a factor of the polynomial x²-kx+14 then the value of k is:

a. -9                                                  b. 9

c. -2           d. 14

Solution: 

‍(a) -9

‍Explanation:

‍if (x+2) is a factor of the polynomial

substituting x=−2 into f(x) must make f(x)=0.

f(x)=x²−kx+14

f(−2)=(−2)²−k(−2)+14

f(−2)=4+2k+14

f(−2)=18+2k

18+2k=0

2k=−18

k=−9

4. The value of the polynomial 5x – 4x² + 3, when x = –1 is:

a. – 6                                                  b. 6

c. 2           d. –2

Solution: 

(a) -6

Explanation:

f(x)=5x−4x²+3

f(−1)=5(−1)−4(−1)²+3

f(−1)=−5−4(1)+3

f(−1)=−5−4+3

f(−1)=−6

5. Assertion: The polynomial p(x) = 5x – 1/2 is a linear polynomial.

Reason: The general form of a linear polynomial is ax + b

a. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion                                                   

b. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion.

c. Assertion is true but the reason is false.

d. Both assertion and reason are false.

Solution:

(a) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion            

Explanation:

Assertion:

"The polynomial p(x)=5x−1/2 is a linear polynomial."

• A polynomial of degree 1 (with the highest power of x being 1) is a linear polynomial.
• The given polynomial p(x)=5x−1/2 is indeed of degree 1, as the highest power of x is 1​
• Therefore, the assertion is true.

Reason:

"The general form of a linear polynomial is ax+b."

• This is correct. The general form of a linear polynomial is ax+b, where aaa and b are constants.
• The given polynomial p(x)=5x−1/2 matches this general form, with a=5 nd b=−1/2
• Therefore, the reason is true.

Polynomial Important Question Class 9: Concepts

A polynomial is an algebraic expression that involves terms connected by addition or subtraction. Each term has a variable raised to a power (exponent). The power of the variable is always a whole number (non-negative integer). Polynomials can have one or more terms.

Definition of Polynomial:

• A polynomial is made up of terms in the form of a_nxⁿ+a_n−1xⁿ⁻¹+...+a₁x+a₀, where:
• a_n​,a_n−1​,...,a_1​,a₀​ are constants (called coefficients).
• x is the variable, and the exponents (powers) are whole numbers.
• The highest power of x is called the degree of the polynomial.

Types of Polynomials

Monomial: A polynomial with just one term. Example: 3x, 5.

Binomial: A polynomial with two terms. Example: x+2, 3x+3

Trinomial: A polynomial with three terms. Example: x²+2x+3

Degree of a Polynomial:

The degree of a polynomial is the highest exponent of the variable. For example, in the polynomial 2x³+5x²+3, the degree is 3.

Zeroes of a Polynomial:

The zeroes or roots of a polynomial are the values of xxx for which the polynomial equals zero. For example, if p(x)=x²−5x+6, the zeroes are the values of x that make p(x)=0. These can be found by factorizing the polynomial.

Factorization of Polynomials:

Polynomials can often be factorized into simpler polynomials. For example,x²−5x+6 can be factorized into (x−2)(x−3).

Remainder Theorem and Factor Theorem:

Remainder Theorem: When a polynomial is divided by x−a, the remainder is the value of the polynomial at x=a.

Factor Theorem: If x−a is a factor of a polynomial, then the polynomial will give a remainder of zero when divided by x−a.

Graph of a Polynomial:

The graph of a polynomial function can be smooth or curved. The shape of the graph depends on the degree of the polynomial and the sign of its leading coefficient (the coefficient of the highest degree term).

This chapter teaches you to recognize polynomials, find their zeroes, and factorize them, which are important skills for solving algebraic problems and understanding how different types of expressions behave.

Polynomial Important Question Class 9: Why

Here’s  why Polynomial Important Questions for Class 9 are essential:

Foundation for Higher Studies: 

Polynomials form the basis for many advanced topics in mathematics, such as quadratic equations, calculus, and coordinate geometry. Practising important questions helps in building a solid understanding of these fundamentals.

Exam-Focused Preparation

Important questions are carefully selected based on the previous year's papers, exam trends, and the NCERT curriculum. Solving these ensures you're well-prepared for frequently asked and high-weightage questions in exams.

Concept Reinforcement

Important questions are designed to cover all key concepts, such as:

• Identifying types of polynomials (monomial, binomial, trinomial).
• Finding the degree of a polynomial.
• Applying the Remainder and Factor Theorems.
• Solving for zeroes of polynomials.
• Factorizing polynomials using standard algebraic identities.

Improves Problem-Solving Skills

Regular practice of important questions enhances analytical thinking, helping you approach problems systematically and solve them efficiently.

Boosts Confidence

Familiarity with important and challenging questions reduces anxiety during exams, as you'll already have experience solving similar problems.

Time Management

Practicing a variety of questions improves speed and accuracy, enabling you to complete the exam on time without compromising on quality.

Comprehensive Revision

Important questions act as a quick summary of the entire chapter, ensuring that no major concept is missed during last-minute revision.

Alignment with Marking Scheme

Polynomials Class 9 Imp Questions often align with the CBSE marking scheme, helping you understand how to structure your answers to earn maximum marks.

By focusing on important questions, students can efficiently utilize their time, master essential concepts, and significantly enhance their exam performance. We hope that you practice the above Polynomials Class 9 Extra Questions With Solutions and achieve your dream marks.

All the Best!