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# Frank solutions for Class 10 Mathematics chapter 10 - Remainder And Factor Theorems

#### Frank Frank Class 10 Mathematics Part 2 ## Chapter 10: Remainder And Factor Theorems

Exercise 10.1

#### Chapter 10: Remainder And Factor Theorems Exercise Exercise 10.1 solutions [Page 0]

Find without division, the remainder in the following:

5x2 - 9x + 4 is divided by (x - 2)

Find without division, the remainder in the following:

5x3 - 7x2 +3 is divided by (x-1)

Find without division, the remainder in the following:

8x2 - 2x + 1 is divided by (2x+ 1)

Find without division, the remainder in the following :

x3 + 8x2 + 7x- 11 is divisible by (x+4)

Find without division, the remainder in the following:

2x3 - 3x2 + 6x - 4 is divisible by (2x-3)

Prove by factor theorem that

(x-2) is a factor of 2x3- 7x -2

Prove by factor theorem that

(2x+1) is a factor of 4x3 + 12x2 + 7x +1

Prove by factor theorem that

(3x-2) is a factor of 18x3 - 3x2 + 6x -12

Prove by factor theorem that

(2x - 1) is a factor of 6x3 - x2 - 5x +2

Prove by factor theorem that

(x - 3) is a factor of 5x2 - 21 x +18

Find the values of a and b in the polynomial f(x) = 2x3 + ax2 + bx + 10, if it is exactly divisible by (x+2) and (2x-1).

Using remainder theorem, find the value of m if the polynomial f(x)= x3 + 5x2 -mx +6 leaves a remainder 2m when divided by (x-1),

Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)

Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).

Find the values of a and b when the polynomial f(x)= ax3 + 3x2 +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2).

Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).

Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).

Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.

What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?

What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-1) ?

What number should be subtracted from the polynomial f(x)= 2x3 - 5x2 +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?

What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?

use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3

Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3

Prove that (x - y) is a factor of yz( y2 - z2) + zx( z2 - x2) + xy ( x2 - y2

Prove that (x-3) is a factor of x3 - x2 - 9x +9 and hence factorize it completely.

Prove that  (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.

Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.

A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by  (x - i)(x - 2), the remainder is (-2x + 5).

The polynomial f(x) = ax4 + x3 + bx2 - 4x + c has (x + 1), (x-2) and (2x - 1) as its factors. Find the values of a,b,c, and remaining factor.

## Chapter 10: Remainder And Factor Theorems

Exercise 10.1

#### Frank Frank Class 10 Mathematics Part 2 ## Frank solutions for Class 10 Mathematics chapter 10 - Remainder And Factor Theorems

Frank solutions for Class 10 Maths chapter 10 (Remainder And Factor Theorems) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CISCE Frank Class 10 Mathematics Part 2 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Frank textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10 Mathematics chapter 10 Remainder And Factor Theorems are Factor Theorem, Remainder Theorem, Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.

Using Frank Class 10 solutions Remainder And Factor Theorems exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Frank Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Frank Textbook Solutions to score more in exam.

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