#### Chapters

Chapter 2: Sales Tax and Value Added Tax

Chapter 3: Banking

Chapter 4: Shares and Dividends

Chapter 5: Linear Inequations

Chapter 6: Quadratic Equations

Chapter 7: Problems Based On Quadratic Equations

Chapter 8: Reflection

Chapter 9: Ratio and Proportion

Chapter 10: Remainder And Factor Theorems

Chapter 11: Matrices

Chapter 12: Distance and Section Formulae

Chapter 13: Equation of A Straight Line

Chapter 14: Symmetry

Chapter 15: Similarity

Chapter 16: Loci

Chapter 17: Circles

Chapter 18: Constructions

Chapter 19: Mensuration I

Chapter 20: Mensuration II

Chapter 21: Trigonometric Identities

Chapter 22: Heights and Distances

Chapter 23: Graphical Representations

Chapter 24: Measures Of Central Tendency

Chapter 25: Probability

#### Frank Frank Class 10 Mathematics Part 2

## Chapter 10: Remainder And Factor Theorems

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

Find without division, the remainder in the following:

5x^{2} - 9x + 4 is divided by (x - 2)

Find without division, the remainder in the following:

5x^{3} - 7x^{2} +3 is divided by (x-1)

Find without division, the remainder in the following:

8x^{2} - 2x + 1 is divided by (2x+ 1)

Find without division, the remainder in the following :

x^{3} + 8x^{2} + 7x- 11 is divisible by (x+4)

Find without division, the remainder in the following:

2x^{3} - 3x^{2} + 6x - 4 is divisible by (2x-3)

Prove by factor theorem that

(x-2) is a factor of 2x^{3}- 7x -2

Prove by factor theorem that

(2x+1) is a factor of 4x^{3} + 12x^{2} + 7x +1

Prove by factor theorem that

(3x-2) is a factor of 18x^{3} - 3x^{2} + 6x -12

Prove by factor theorem that

(2x - 1) is a factor of 6x^{3} - x^{2} - 5x +2

Prove by factor theorem that

(x - 3) is a factor of 5x^{2} - 21 x +18

Find the values of a and b in the polynomial f(x) = 2x^{3} + ax^{2} + 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)= x^{3} + 5x^{2} -mx +6 leaves a remainder 2m when divided by (x-1),

Find the value of m ·when x^{3} + 3x^{2} -m x +4 is exactly divisible by (x-2)

Find the values of p and q in the polynomial f(x)= x^{3} - px^{2} + 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)= ax^{3} + 3x^{2} +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)= x^{3} - 2x^{2} + 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)= 2x^{2} -5x +a and g(x)= 2x^{2} + 5x +b both have a factor (2x+1).

Find the values of a and b when the factors of the polynomial f(x)= ax^{3} + bx^{2} + x a are (x+3) and (2x-1). Factorize the polynomial completely.

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

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

What number should be subtracted from the polynomial f(x)= 2x^{3} - 5x^{2} +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?

What number should be added to polynomial f(x)= 12x^{3} + 16x^{2} - 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( y^{2} - z^{2}) + zx( z^{2} - x^{2}) + xy ( x^{2} - y^{2})

Prove that (x-3) is a factor of x^{3} - x^{2} - 9x +9 and hence factorize it completely.

Prove that (x+ 1) is a factor of x^{3} - 6x^{2} + 5x + 12 and hence factorize it completely.

Prove that (5x - 4) is a factor of the polynomial f(x) = 5x^{3} - 4x^{2} - 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) = ax^{4} + x^{3} + bx^{2} - 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

#### Frank Frank Class 10 Mathematics Part 2

#### Textbook solutions for Class 10

## 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.

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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.

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