Polynomials Class 9 important questions with answers PDF download
Chapter 2 of Class 9 Maths Polynomials, introduces students to the concept of polynomials, their types, and their properties. This chapter covers key concepts according to the Latest Class 9 Maths Syllabus like the degree of a polynomial, coefficients, zeroes of polynomials, and the relationship between the coefficients and zeroes. The Important Questions for Chapter 2 - Polynomials is designed to help students practice and master the key concepts of this chapter. By solving these important questions, students can reinforce their understanding, improve their problem-solving skills, and gain confidence in tackling various polynomial problems in exams. Whether you're preparing for unit tests, term exams, or the final board exam, these questions are carefully curated to help you excel in your studies. Practising these Class 9 Maths Important Questions PDF will ensure that you’re well-prepared to face the challenges of this chapter.
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FAQs on CBSE Important Questions for Class 9 Maths Polynomials - 2025-26
1. What are the high-weightage topics in Class 9 Maths Chapter 2, Polynomials, for the 2025-26 exam?
For the CBSE Class 9 Maths exam 2025-26, the most important topics in Polynomials that frequently carry higher marks are:
- Factorisation of Polynomials: This includes factorising quadratic polynomials by splitting the middle term and cubic polynomials using the Factor Theorem. These are often asked as 3 or 4-mark questions.
- Algebraic Identities: Questions involving the application of identities like (x + y + z)², (x ± y)³, and especially x³ + y³ + z³ – 3xyz are critical and often appear in the higher marks section.
- Remainder Theorem and Factor Theorem: Expect direct questions to find the remainder or to check if a linear polynomial is a factor of another polynomial. These concepts are fundamental for solving more complex problems.
2. What types of factorisation questions from Polynomials can I expect for 3 or 5 marks?
In the exam, factorisation questions from Polynomials are typically structured by difficulty and marks:
- For 3 marks: You can expect questions on factorising a quadratic polynomial of the form ax² + bx + c by splitting the middle term. Another common type is to use an algebraic identity like a³ - b³ to factorise an expression.
- For 5 marks: The most common long-answer question is the factorisation of a cubic polynomial. This requires a multi-step process: first, find one zero using the Factor Theorem (by trial and error), then perform polynomial division, and finally, factorise the resulting quadratic quotient.
3. How should I correctly apply the Remainder and Factor Theorems to solve exam questions?
To apply these theorems correctly and secure full marks, follow this approach:
- Remainder Theorem: When asked to find the remainder when a polynomial p(x) is divided by a linear polynomial (x - a), you do not need to perform long division. Simply calculate the value of p(a). The result is the remainder. Clearly state the theorem in your answer.
- Factor Theorem: To check if (x - a) is a factor of p(x), calculate p(a). If p(a) = 0, then (x - a) is a factor. If p(a) ≠ 0, it is not. This theorem is the first step in factorising cubic polynomials.
4. What is the key difference between the 'zero of a polynomial' and the 'value of a polynomial'?
Understanding this difference is crucial for avoiding errors. The value of a polynomial, p(x), is the result you get when you substitute a specific number for the variable x. However, a zero of a polynomial is a specific value of the variable for which the value of the polynomial becomes zero. For example, for p(x) = x - 2, the value of the polynomial at x=5 is 3, but the zero of the polynomial is 2, because p(2) = 0.
5. What is a common mistake students make when applying algebraic identities to factorise polynomials?
A very common mistake, besides incorrect formula recollection, is with signs, especially when using identities like (x - y)³ or x³ - y³. Students often misplace the negative signs in the expanded form. For the identity x³ + y³ + z³ - 3xyz, a frequent error is failing to correctly identify the terms for 'x', 'y', and 'z' when the expression involves negative terms, such as factorising 8a³ - b³ + 27c³ + 18abc.
6. How does the Factor Theorem build upon the Remainder Theorem?
The Factor Theorem is a special case of the Remainder Theorem. The Remainder Theorem states that when a polynomial p(x) is divided by (x-a), the remainder is p(a). The Factor Theorem takes this one step further: if that remainder p(a) happens to be zero, then (x-a) must be a perfect factor of p(x). Essentially, the Factor Theorem gives a specific meaning to a zero remainder, connecting it directly to the concept of factorisation.
7. Which types of questions on 'degree of a polynomial' are expected in the Class 9 exam?
Questions about the degree of a polynomial are usually short, often for 1 or 2 marks. Common formats include:
- Identifying the degree of a given polynomial, especially one with multiple variables or terms that are not in standard order.
- Finding the degree of a product or sum of two polynomials.
- Multiple Choice Questions (MCQs) asking to classify a polynomial as linear, quadratic, or cubic based on its degree.
- Questions that test the concept that the degree of a non-zero constant polynomial is zero.
8. What is the most important algebraic identity in the Polynomials chapter for long-answer questions?
The most crucial identity for 5-mark questions is x³ + y³ + z³ – 3xyz = (x + y + z)(x² + y² + z² – xy – yz – zx). Questions based on this identity are often complex and test multiple skills. A typical problem might ask you to evaluate an expression without direct calculation, using the special condition: if x + y + z = 0, then x³ + y³ + z³ = 3xyz. Be prepared to identify 'x', 'y', and 'z' from a given expression to apply this identity effectively.
