ICSE Class 10CISCE
Account
It's free!

User


Login
Create free account


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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

Chapters

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10

Chapter 8 - Remainder and Factor Theorems

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’. 

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. 

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 

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

 2x3 + x2 – 13x + 6 

Page 0

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

 3x3 + 2x2 – 23x – 30

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

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. 

Selina Selina ICSE Concise Mathematics Class 10

Selina ICSE Concise Mathematics for Class 10
S