ICSE 10 Maths
Remainder and Factor Theorems
Question 1:
Find the value of ‘a’, if (x – a) is a factor of – a
+ x + 2. [Level: Easy]
Question 2:
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8. [Level: Moderate]
Question 3:
The polynomials a + 3
– 3 and 2
– 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a. [Level: Moderate]
Question 4:
Find the number that must be subtracted from the polynomial 3 +
– 22y + 15, so that the resulting polynomial is completely divisible by y + 3. [Level: Moderate]
Question 5:
If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x. Level: [Difficult]
Question 6:
When + 3
– mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m. [Level: Easy]
Question 7:
What should be subtracted from 3 – 8
+ 4x – 3, so that the resulting expression has x + 2 as a factor? [Level: Moderate]
Question 8:
If x – 2 is a factor of + ax + b and a + b = 1, find the values of a and b. [Level: Difficult]
Question 9:
Find the value of ‘m’, if m + 2
– 3 and
– mx + 4 leave the same remainder when each is divided by x – 2. [Level: Difficult]
Question 10:
Find the number which should be added to + x + 3 so that the resulting polynomial is completely divisible by (x + 3). [Level: Moderate]
Question 11:
When the polynomial + 2
– 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial
+ a
– 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0. [Level: Difficult]
Question 12:
When divided by x – 3 the polynomials – p
+ x + 6 and 2
–
– (p + 3) x – 6 leave the same remainder. Find the value of ‘p’. [Level: Moderate]
Question 13:
Using remainder theorem, find the value of k if on dividing 2 + 3
– kx + 5 by x – 2, leaves a remainder 7. [Level: Moderate]
Question 14:
What must be subtracted from 16 – 8
+ 4x + 7 so that the resulting expression has 2x + 1 as a factor? [Level: Difficult]
Question 15:
Show that is a factor of 5
. [Level: Easy]
Question 16:
Find the value of k, if 3x – 4 is a factor of expression 3 + 2x – k. [Level: Moderate]
Question 17:
When + 2
– kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k. [Level: Easy]
Question 18:
If x + a is a common factor of expressions f(x) = + px + q and g(x) =
+ mx + n; show that
. [Level: Moderate]
Question 19:
Find the value of k, if 2x + 1 is a factor of (3k + 2) + (k – 1). [Level: Easy]
Question 20:
Find the values of m and n so that x – 1 and x + 2 both are factors of + (3m + 1)
+ nx – 18. [Level: Moderate]
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In summary, problem-solving after learning a theoretical concept on CBSE Remainder and Factor Theorems ICSE 10 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.
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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 ICSE 10 Maths Remainder and Factor Theorems NCERT Chapter 8
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 ICSE 10 Maths Remainder and Factor Theorems NCERT Chapter 8 useful.
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