#### Chapters

Chapter 2: Banking (Recurring Deposit Account)

Chapter 3: Shares and Dividend

Chapter 4: Linear Inequations (In one variable)

Chapter 5: Quadratic Equations

Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)

Chapter 7: Ratio and Proportion (Including Properties and Uses)

Chapter 8: Remainder and Factor Theorems

Chapter 9: Matrices

Chapter 10: Arithmetic Progression

Chapter 11: Geometric Progression

Chapter 12: Reflection

Chapter 13: Section and Mid-Point Formula

Chapter 14: Equation of a Line

Chapter 15: Similarity (With Applications to Maps and Models)

Chapter 16: Loci (Locus and Its Constructions)

Chapter 17: Circles

Chapter 18: Tangents and Intersecting Chords

Chapter 19: Constructions (Circles)

Chapter 20: Cylinder, Cone and Sphere

Chapter 21: Trigonometrical Identities

Chapter 22: Height and Distances

Chapter 23: Graphical Representation

Chapter 24: Measure of Central Tendency(Mean, Median, Quartiles and Mode)

Chapter 25: Probability

## Chapter 8: Remainder and Factor Theorems

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 8 Remainder and Factor Theorems Exercise Exercise 8(A) [Pages 108 - 109]

Find , in given case, the remainder when :

`x^4-3x^2+2x+1` is dividend by x-1

Find, in given case, the remainder when:

`x^3+3x^2-12x+4` is divided by x-2

Find , in given case the remainder when:

`x^4+1` is divided by x+1

show that

`x-2` is a factor of `5x^2+15x-50`

show that

`3x+2` is a factor of `3x^2-x-2`

Use the Remainder Theorem to find which of the following is a factor of 2x^{3} + 3x^{2} – 5x – 6.

x + 1

Use the Remainder Theorem to find which of the following is a factor of 2x^{3} + 3x^{2} – 5x – 6.

2x – 1

Use the Remainder Theorem to find which of the following is a factor of 2x^{3} + 3x^{2} – 5x – 6.

x + 2

If 2x + 1 is a factor of 2x^{2} + ax – 3, find the value of a.

Find the value of k, if 3x – 4 is a factor of expression `3x^2` + 2x − k.

Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x^{3} + ax^{2} + bx – 12.

Find the value of k, if 2x + 1 is a factor of (3k + 2)x^{3} + (k − 1)

Find the value of a, if x – 2 is a factor of 2x^{5} – 6x^{4} – 2ax^{3} + 6ax^{2} + 4ax + 8.

Find the values of m and n so that x – 1 and x + 2 both are factors of x^{3} + (3m + 1) x^{2} + nx – 18.

When `x^3 + 2x ^2– kx + 4 `is divided by x – 2, the remainder is k. Find the value of constant k.

Find the value of a, if the division of ax^{3} + 9x^{2} + 4x – 10 by x + 3 leaves a remainder 5.

If x^{3} + ax^{2} + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.

The expression 2x^{3} + ax^{2} + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b

What number should be added to 3x^{3} – 5x^{2} + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?

What number should be subtracted from x^{3} + 3x^{2} – 8x + 14 so that on dividing it with x – 2, the remainder is 10.

The polynomials 2x^{3} – 7x^{2} + ax – 6 and x^{3} – 8x^{2} + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’.

If (x – 2) is a factor of the expression 2x^{3} + ax^{2} + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b

Find ‘a‘ if the two polynomials ax^{3} + 3x^{2} – 9 and 2x^{3} + 4x + a, leave the same remainder when divided by x + 3.

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 8 Remainder and Factor Theorems Exercise Exercise 8(B) [Pages 111 - 112]

Using the Factor Theorem, show that:

(x – 2) is a factor of x^{3} – 2x^{2} – 9x + 18. Hence, factorise the expression x^{3} – 2x^{2} – 9x + 18 completely.

(x + 5) is a factor of 2x^{3} + 5x^{2} – 28x – 15. Hence, factorise the expression 2x^{3} + 5x^{2} – 28x – 15 completely.

(3x + 2) is a factor of 3x^{3} + 2x^{2} – 3x – 2. Hence, factorise the expression 3x^{3} + 2x^{2} – 3x – 2 completely.

Using the Remainder Theorem, factorise each of the following completely.

3x^{3 }+ 2x^{2} − 19x + 6

Using the Reminder Theorem, factorise of the following completely.

2x^{3} + x^{2} – 13x + 6

Using the Remainder Theorem, factorise each of the following completely.

3x^{3} + 2x^{2} – 23x – 30

Using the Remainder Theorem, factorise each of the following completely.

4x^{3} + 7x^{2} – 36x – 63

Using the Remainder Theorem, factorise each of the following completely

x^{3} + x^{2} – 4x – 4

Using the Remainder Theorem, factorise the expression 3x^{3} + 10x^{2} + x – 6. Hence, solve the equation 3x^{3} + 10x^{2} + x – 6 = 0.

Factorise the expression f (x) = 2x^{3} – 7x^{2} – 3x + 18. Hence, find all possible values of x for which f(x) = 0.

Given that x – 2 and x + 1 are factors of f(x) = x^{3} + 3x^{2} + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

The expression 4x^{3} – bx^{2} + x – c leaves remainders 0 and 30 when divided by x + 1 and 2x – 3 respectively. Calculate the values of b and c. Hence, factorise the expression completely.

If x + a is a common factor of expressions f(x) = x^{2} + px + q and g(x) = x^{2} + mx + n;

show that : `a=(n-q)/(m-p)`

The polynomials ax^{3} + 3x^{2} – 3 and 2x^{3} – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.

Find the value of ‘a’, if (x – a) is a factor of x^{3} – ax^{2} + x + 2.

Find the number that must be subtracted from the polynomial 3y^{3} + y^{2} – 22y + 15, so that the resulting polynomial is completely divisible by y + 3.

#### Selina solutions for Concise Mathematics Class 10 ICSE Chapter 8 Remainder and Factor Theorems Exercise Exercise 8(C) [Page 112]

Show that (x – 1) is a factor of x^{3} – 7x^{2} + 14x – 8. Hence, completely factorise the given expression.

Using Remainder Theorem, factorise:

x^{3} + 10x^{2} – 37x + 26 completely

When x^{3} + 3x^{2} – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.

What should be subtracted from 3x^{3} – 8x^{2} + 4x – 3, so that the resulting expression has x + 2 as a factor?

If (x + 1) and (x – 2) are factors of x^{3} + (a + 1)x^{2} – (b – 2)x – 6, find the values of a and b. And then, factorise the given expression completely.

if x – 2 is a factor of x^{2} + ax + b and a + b = 1, find the values of a and b.

Factorise x^{3} + 6x^{2} + 11x + 6 completely using factor theorem.

Find the value of ‘m’, if mx^{3} + 2x^{2} – 3 and x^{2} – mx + 4 leave the same remainder when each is divided by x – 2

The polynomial px^{3} + 4x^{2} – 3x + q is completely divisible by x^{2} – 1; find the values of p and q. Also, for these values of p and q factorize the given polynomial completely.

Find the number which should be added to x^{2} + x + 3 so that the resulting polynomial is completely divisible by (x + 3).

When the polynomial x^{3} + 2x^{2} – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x^{3} + ax^{2} – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.

(3x + 5) is a factor of the polynomial (a – 1)x^{3} + (a + 1)x^{2} – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.

When divided by x – 3 the polynomials x^{3} – px^{2} + x + 6 and 2x^{3} – x^{2} – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.

Using the Remainder Theorem, factorise each of the following completely.

2x^{3} + x^{2} – 13x + 6

Using remainder theorem, find the value of k if on dividing 2x^{3} + 3x^{2} - kx + 5 by x - 2, leaves a remainder 7

What must be subtracted from 16x^{3} – 8x^{2} + 4x + 7 so that the resulting expression has

2x + 1 as a factor?

## Chapter 8: Remainder and Factor Theorems

## Selina solutions for Concise Mathematics Class 10 ICSE chapter 8 - Remainder and Factor Theorems

Selina solutions for Concise Mathematics Class 10 ICSE chapter 8 (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 Concise Mathematics Class 10 ICSE solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Concise Mathematics Class 10 ICSE chapter 8 Remainder and Factor Theorems are Factor Theorem, Remainder Theorem, Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem.

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