Toppers Study Toppers Study Toppers StudyDetailed NCERT Solutions for 9 Mathematics 2. Polynomials to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Detailed NCERT Solutions for 9 Mathematics 2. Polynomials to simplify learning. Understand chapters clearly and practice with free solutions for better results.
Preparing for exams becomes easier with Exercise 2.3. Whether you are studying for board exams or mid-term exams, 9 Mathematics Chapter 2. Polynomials solutions provide quick revising points, well-structured answers, and additional practice material to help you score better.
ncert_solutionsChapter 2. Polynomials
Exercise 2.3
Solution:
(i)By remainder theorem, the required remainder is equal to p(x) = (-1)
P (-1) = x3+ 3x2+ 3x+1
= (-1)3 + 3 (-1)2 + 3(-1) + 1
= -1 + 3 – 3 + 1 = 0
Required remainder is p (-1) = 0
Required remainder is p (1/2) = 0
(iv) By remainder theorem, the required remainder is equal to p(x) = - π
P(x) = x3+ 3x2+ 3x+1
P(π) = (- π)3 + 3(-π)2 + 3(-π) + 1
= (-π)3 + 3π2 + 3π + 1
Required remainder is p (π) = 0
Required remainder is p (- 5/2) = 0
Q.2. find the remainder when x3- ax2 + 6x - a is divided by x- a.
Solution: Let P(x) = x3- ax2+ 6x- a . P(x) = a.
By remainder theorem
P (a) = (a)3- a(a)2+ 6(a) - a
=a3-a3 + 6a - a
Remainder = 5a
Q3. Check whether 7 + 3x is a factor of 3x3 + 7x.
Solution:
g(x) = 7 + 3x = 0
⇒ 3x = - 7
P(x) ≠ 0
Therefore, 7 + 3x is not a factor of P(x).
Exercise 2.3 are created by experts to give step-by-step explanations. Around 60–70% of exam questions are based on NCERT concepts. Our 9 Mathematics Chapter 2. Polynomials solutions help you understand the core concepts and practice effectively.
Revision is the key to exam success. Our notes for 9 Mathematics highlight important formulas, key definitions, and exam-ready points from Chapter 2. Polynomials. These quick revision notes make last-minute preparation easy.
Every NCERT chapter ends with exercises, and solving them is crucial. Our Exercise 2.3 include complete solutions for 9 Mathematics Chapter 2. Polynomials exercises. With step-by-step answers, you gain clarity and confidence to attempt similar exam questions.
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Our Exercise 2.3 are useful for both board exams and mid-term exams. For 9 Mathematics, we provide notes, exercises, and important Q&A so that you can revise smartly and write perfect answers in exams.
In short, Exercise 2.3 for 9 Mathematics Chapter 2. Polynomials are a complete study package. With quick revising points, NCERT exercises, and additional important questions, you can prepare effectively for exams. Make these solutions your study companion and excel in your academic journey.
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