Daily Practice Problems Polynomials

Question 1:

Find the degree of each of the polynomials given below:

(i) x⁵ – x⁴ + 3 (ii) 2 – y² – y³ + 2y⁸ (iii) 2

Question 2:

Factorise: (a – b)³ + (b – c)³ + (c – a)³

Question 3:

If x² – 3x + 2 divides x³ – 6x² + ax + b exactly, then find the value of ‘a’ and ‘b’

Question 4:

Factorise: 125x³ – 64y³

Question 5:

If p(x) = x² – 2√2x + 1, then find the value of p(2√2).

Question 6:

Find the value of m, if x + 4 is a factor of the polynomial x² + 3x + m.

Question 7:

If 3x + 2y = 12 and xy = 6, find the value of 27x³ + 8y³.

Question 8:

If one zero of the polynomial x² – 13x + 40 is 5, which is the other zero?

Question 9:

If x – 3 is a factor of x² – 6x + 12, then find the value of k. Also, find the other factor of the polynomial for this value of k.

Question 10:

What must be added to polynomial f(x) = x⁴ + 2x³ – 2x² + x – 1 so that resulting polynomial is exactly divisible by x² + 2x – 3?

Question 11:

Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Question 12:

Using suitable identity, evaluate the following:

(i) 98³ (ii) 188 * 212

Question 13:

Write the coefficients of x² in each of the following:

(i) 2 - x² + x (ii) x –

Question 14:

Which of the following expressions are polynomial in one variable and which are not?

(i) 3x² – 4x + 15 (ii) y² + 2√3 (iii) 3√x - x√2 (iv) x^-1 + 3x

Question 15:

Without actually calculating the cubes, find the value of (-12)³ + (7)³ + (5)³

Question 16:

Check whether -2 and 2 are zeroes of the polynomial x² - 2.

Question 17:

The zeroes of the polynomial p(x) = x(x - 2)(x + 3) are _____.

Question 18:

Find the value of the polynomial 5x – 4x² + 3 at

(i) x = 0 (ii) x = -1

Question 19:

Using suitable identity, factorize

(i) –

(ii) –

Question 20:

Write (3a + 4b + 5c)² in expanded form.

**********

Problem-solving on Class 9 Maths Polynomials NCERT Chapter 2 after learning a theoretical concept is crucial for several reasons:

Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 9 Maths Polynomials you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 9 Maths Polynomials NCERT Chapter 2, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Polynomials Class 9 Maths in practical scenarios helps you remember them better than passive reading or memorization.
Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Polynomials Class 9 Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Polynomials. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Polynomials Class 9 Maths Online Tests at LearnoHub.com.
Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Polynomials Class 9 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on Class 9 Maths Polynomials NCERT Chapter 2

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 9 Maths Polynomials NCERT Chapter 2 useful.

Last but not least, to get the best hold on Class 9 Maths Polynomials NCERT Chapter 2, do not forget to check out:

Polynomials Class 9 Maths Best videos
Polynomials Class 9 Maths NCERT Solutions
Class 9 Maths Polynomials Revision notes
Polynomials Class 9 Maths DPPs, Download PDF of solutions
Class 9 Maths Polynomials Online Tests
Class 9 Maths Sample papers