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# Frank solutions for ICSE Class 10 Mathematics Part 2 chapter 10 - Remainder And Factor Theorems [Latest edition]

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#### Chapters ## Chapter 10: Remainder And Factor Theorems

Exercise 10.1

### Frank solutions for ICSE Class 10 Mathematics Part 2 Chapter 10 Remainder And Factor Theorems Exercise 10.1

Exercise 10.1 | Q 1.1

Find without division, the remainder in the following:

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

Exercise 10.1 | Q 1.2

Find without division, the remainder in the following:

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

Exercise 10.1 | Q 1.3

Find without division, the remainder in the following:

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

Exercise 10.1 | Q 1.4

Find without division, the remainder in the following :

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

Exercise 10.1 | Q 1.5

Find without division, the remainder in the following:

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

Exercise 10.1 | Q 2.1

Prove by factor theorem that

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

Exercise 10.1 | Q 2.2

Prove by factor theorem that

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

Exercise 10.1 | Q 2.3

Prove by factor theorem that

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

Exercise 10.1 | Q 2.4

Prove by factor theorem that

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

Exercise 10.1 | Q 2.5

Prove by factor theorem that

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

Exercise 10.1 | Q 3

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).

Exercise 10.1 | Q 4

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),

Exercise 10.1 | Q 5

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

Exercise 10.1 | Q 6

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).

Exercise 10.1 | Q 7

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).

Exercise 10.1 | Q 8

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).

Exercise 10.1 | Q 9

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).

Exercise 10.1 | Q 10

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.

Exercise 10.1 | Q 11

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

Exercise 10.1 | Q 12

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

Exercise 10.1 | Q 13

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)?

Exercise 10.1 | Q 14

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

Exercise 10.1 | Q 15

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

Exercise 10.1 | Q 16

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

Exercise 10.1 | Q 17

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

Exercise 10.1 | Q 18

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

Exercise 10.1 | Q 19

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

Exercise 10.1 | Q 20

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

Exercise 10.1 | Q 21

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).

Exercise 10.1 | Q 22

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

Frank solutions for ICSE Class 10 Mathematics Part 2 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 ICSE Class 10 Mathematics Part 2 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in ICSE Class 10 Mathematics Part 2 chapter 10 Remainder And Factor Theorems are Factor Theorem, Remainder Theorem, Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.

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