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

## Chapter 8: Remainder and Factor Theorems

Ex. 8AEx. 8BEx. 8C

#### Chapter 8: Remainder and Factor Theorems Exercise 8A solutions [Page 0]

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 2x3 + 3x2 – 5x – 6.

x + 1

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

2x – 1

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

x + 2

If 2x + 1 is a factor of 2x2 + 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 x3 + ax2 + bx – 12.

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

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

Find the values of m and n so that x – 1 and x + 2 both are factors of x3 + (3m + 1) x2 + 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 ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.

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.

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

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

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

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’.

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

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

#### Chapter 8: Remainder and Factor Theorems Exercise 8B solutions [Page 0]

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.

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

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

Using the factor Theorem, show that:

(iv) 2x + 7 is a factor 2x3 + 5x2 − 11x – 14. Hence, factorise the given expression completely.

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

3x+ 2x2 − 19x + 6

Using the Reminder Theorem, factorise of the following completely.

2x3 + x2 – 13x + 6

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

3x3 + 2x2 – 23x – 30

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

4x3 + 7x2 – 36x – 63

Using the Remainder Theorem, factorise each of the following completely

x3 + x2 – 4x – 4

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

Factorise the expression f (x) = 2x3 – 7x2 – 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) = x3 + 3x2 + ax + b; calculate the values of a and b. Hence, find all the factors of f(x).

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.

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)

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.

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

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.

#### Chapter 8: Remainder and Factor Theorems Exercise 8C solutions [Page 0]

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

Using remainder Theorem, factorise:

2x3 + 7x2 − 8x – 28 Completely

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

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

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.

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

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

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

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.

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

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.

(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.

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’.

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

2x3 + x2 – 13x + 6

## Chapter 8: Remainder and Factor Theorems

Ex. 8AEx. 8BEx. 8C

## 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 (2018-2019) solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. Selina textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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

Using Selina Class 10 solutions Remainder and Factor Theorems exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Selina Solutions are important questions that can be asked in the final exam. Maximum students of CISCE Class 10 prefer Selina Textbook Solutions to score more in exam.

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