#### 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

## 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

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

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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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