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Selina solutions for Class 10 Maths chapter 8 - Remainder and Factor Theorems

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Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10 - Shaalaa.com

Chapter 8: Remainder and Factor Theorems

Exercise 8(A)Exercise 8(B)Exercise 8(C)

Selina solutions for Class 10 Maths Chapter 8 Exercise Exercise 8(A) [Pages 108 - 109]

Exercise 8(A) | Q 1.1 | Page 108

Find , in given case, the remainder when : 

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

Exercise 8(A) | Q 1.2 | Page 108

Find, in given case, the remainder when: 

`x^3+3x^2-12x+4` is divided by x-2 

Exercise 8(A) | Q 1.3 | Page 108

Find , in given case the remainder when: 

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

Exercise 8(A) | Q 2.1 | Page 108

show that 

`x-2` is a factor of `5x^2+15x-50`  

Exercise 8(A) | Q 2.2 | Page 108

show that 

`3x+2` is a factor of `3x^2-x-2` 

Exercise 8(A) | Q 3.1 | Page 108

Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6. 

x + 1

Exercise 8(A) | Q 3.2 | Page 108

Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6. 

2x – 1 

Exercise 8(A) | Q 3.3 | Page 108

Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6. 

x + 2

Exercise 8(A) | Q 4.1 | Page 108

If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.

Exercise 8(A) | Q 4.2 | Page 108

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

Exercise 8(A) | Q 5 | Page 108

Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.

Exercise 8(A) | Q 6 | Page 108

Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1)

Exercise 8(A) | Q 7 | Page 108

Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8. 

Exercise 8(A) | Q 8 | Page 108

Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1) x2 + nx – 18.

Exercise 8(A) | Q 9 | Page 108

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

Exercise 8(A) | Q 10 | Page 109

Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.

Exercise 8(A) | Q 11 | Page 109

If x3 + ax2 + 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.

Exercise 8(A) | Q 12 | Page 109

The expression 2x3 + ax2 + bx – 2 leaves remainder 7 and 0 when divided by 2x – 3 and x + 2 respectively. Calculate the values of a and b

Exercise 8(A) | Q 13 | Page 109

What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8? 

Exercise 8(A) | Q 14 | Page 109

What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it with x – 2, the remainder is 10. 

Exercise 8(A) | Q 15 | Page 109

The polynomials 2x3 – 7x2 + ax – 6 and x3 – 8x2 + (2a + 1)x – 16 leaves the same remainder when divided by x – 2. Find the value of ‘a’. 

Exercise 8(A) | Q 16 | Page 109

If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b

Exercise 8(A) | Q 17 | Page 109

Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3. 

Selina solutions for Class 10 Maths Chapter 8 Exercise Exercise 8(B) [Pages 111 - 112]

Exercise 8(B) | Q 1.1 | Page 111

Using the Factor Theorem, show that:

 (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.

Exercise 8(B) | Q 1.2 | Page 111

(x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.  

Exercise 8(B) | Q 1.3 | Page 112

 (3x + 2) is a factor of 3x3 + 2x2 – 3x – 2. Hence, factorise the expression 3x3 + 2x2 – 3x – 2 completely.

Exercise 8(B) | Q 2.1 | Page 112

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

3x+ 2x2 − 19x + 6 

Exercise 8(B) | Q 2.2 | Page 112

Using the Reminder Theorem, factorise of the following completely.

2x3 + x2 – 13x + 6

Exercise 8(B) | Q 2.3 | Page 112

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

 3x3 + 2x2 – 23x – 30

Exercise 8(B) | Q 2.4 | Page 112


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

4x3 + 7x2 – 36x – 63

Exercise 8(B) | Q 2.5 | Page 112

Using the Remainder Theorem, factorise each of the following completely 

 x3 + x2 – 4x – 4

Exercise 8(B) | Q 3 | Page 112

Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0. 

Exercise 8(B) | Q 4 | Page 112

Factorise the expression f (x) = 2x3 – 7x2 – 3x + 18. Hence, find all possible values of x for which f(x) = 0.

Exercise 8(B) | Q 5 | Page 112

Given that x – 2 and x + 1 are factors of f(x) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

Exercise 8(B) | Q 6 | Page 112

The expression 4x3 – bx2 + 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. 

Exercise 8(B) | Q 7 | Page 112

If x + a is a common factor of expressions f(x) = x2 + px + q and g(x) = x2 + mx + n; 

show that : `a=(n-q)/(m-p)` 

Exercise 8(B) | Q 8 | Page 112

The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a. 

Exercise 8(B) | Q 9 | Page 112

Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.

Exercise 8(B) | Q 10 | Page 112

Find the number that must be subtracted from the polynomial 3y3 + y2 – 22y + 15, so that the resulting polynomial is completely divisible by y + 3. 

Selina solutions for Class 10 Maths Chapter 8 Exercise Exercise 8(C) [Page 112]

Exercise 8(C) | Q 1 | Page 112

Show that (x – 1) is a factor of x3 – 7x2 + 14x – 8. Hence, completely factorise the given expression.

Exercise 8(C) | Q 2 | Page 112

Using Remainder Theorem, factorise:
x3 + 10x2 – 37x + 26 completely

Exercise 8(C) | Q 3 | Page 112

When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m. 

Exercise 8(C) | Q 4 | Page 112

What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor? 

Exercise 8(C) | Q 5 | Page 112

If (x + 1) and (x – 2) are factors of x3 + (a + 1)x2 – (b – 2)x – 6, find the values of a and b. And then, factorise the given expression completely.

Exercise 8(C) | Q 6 | Page 112

if x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.

Exercise 8(C) | Q 7 | Page 112

Factorise x3 + 6x2 + 11x + 6 completely using factor theorem. 

Exercise 8(C) | Q 8 | Page 112

Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2

Exercise 8(C) | Q 9 | Page 112

The polynomial px3 + 4x2 – 3x + q is completely divisible by x2 – 1; find the values of p and q. Also, for these values of p and q factorize the given polynomial completely.

Exercise 8(C) | Q 10 | Page 112

Find the number which should be added to x2 + x + 3 so that the resulting polynomial is completely divisible by (x + 3).

Exercise 8(C) | Q 11 | Page 112

When the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.

Exercise 8(C) | Q 12 | Page 112

(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely. 

Exercise 8(C) | Q 13 | Page 112

When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.

Exercise 8(C) | Q 14 | Page 112

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

 2x3 + x2 – 13x + 6 

Exercise 8(C) | Q 15 | Page 112

Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 - kx + 5 by x - 2, leaves a remainder 7

Exercise 8(C) | Q 16 | Page 112

What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has
2x + 1 as a factor?

Chapter 8: Remainder and Factor Theorems

Exercise 8(A)Exercise 8(B)Exercise 8(C)

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10 - Shaalaa.com

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

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

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Concepts covered in Class 10 Mathematics 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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