S Chand ICSE Maths Solutions Class 10 Chapter 7 Factor Theorem Factorization

Hi students, Welcome to Amans Maths Blogs (AMB). In this post, you will get S Chand ICSE Maths Solutions Class 10 Chapter 7 Factor Theorem Factorization. This is seventh chapter ‘Factor Theorem and Factorization‘ included in ICSE Class 10 Maths syllabus.

S Chand ICSE Maths Solutions Class 10 Chapter 7 Factor Theorem Factorization Exercise 7

ICSE Solutions Factor Theorem Factorization Exercise 7: Ques No 1

Find the remainder when the expression

(i) 3x³ + 8x² – 6x + 1 is divided by (x + 3)

(ii) 5x³ – 8x² + 3x – 4 is divided by (x – 1)

(iii) x³ + 3x² – 1 is divided by (3x + 2)

(ii) 4x³ – 12x² + 14x – 3 is divided by (2x – 1)

S Chand ICSE Math Class 10 Solutions 1(i):

Solutions 1(ii):

Solutions 1(iii):

Solutions 1(iv):

Ques No 2

When x³ + 3x² – kx + 4 is divided by (x – 2), the remainder is k. Find the value of constant k.

Solutions:

Ques No 3

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

Solutions:

Ques No 4

If the polynomials ax³ + 4x² + 3x – 4 and x³ – 4x – a leave the same remainder when divided by (x – 2), find the value of a.

Solutions:

Ques No 5

Use factor theorem in each of the following to find whether g(x) is factor of f(x) or not.

(i) f(x) = x³ – 6x² + 11x – 6, g(x) = x – 3

(ii) f(x) = 2x³ – 9x² + x + 12, g(x) = x + 1

(iii) f(x) = 7x² – 2√8x² – 6, g(x) = x + √2

(iv) f(x) = 3x³ + x² – 20x + 12, g(x) = 3x – 2

Solutions 5(i):

Solutions 5(ii):

Solutions 5(iii):

Solutions 5(iv):

Ques No 6

Find the value of a if x³ + ax² + 2a – 2 is exactly divisible by (x + 1).

Solutions:

Ques No 7

Find the values of a and b so that the expression x³ + 10x² + ax + b is exactly divisible by (x – 1) as well as (x – 2).

Solutions:

Ques No 8

If (x – 2) is a factor of x² + ax – 6 = 0 and x² – 9x + b = 0, find the value of a and b.

Solutions:

Ques No 9

If both (x – 2) and (x – 1/2) are factors of px² + 5x + r, show that p = r.

Solutions:

Ques No 10

If x³ + ax² + bx + 6 has (x – 2) as a factor and leaves a remainder 3 when divided by (x – 3), find the value of a and b.

Solutions:

Ques No 11

Factorize:

(i) x³ + 13x² + 32x + 20 if it is given that (x + 2) as its factor.

(ii) 4x³ + 20x² + 33x + 18 if it is given that (2x + 3) as its factor.

Solutions 11(i):

Solutions 11(ii):

Ques No 12

Show that

(i) (x – 10) is a factor of x³ – 23x² + 142x – 120 and hence factorize it completely.

(ii) (3z + 10) is a factor of 9z³ – 27z² – 100z + 300 and hence factorize it completely.

Solutions 12(i):

Solutions 12(i):

Ques No 13

Given that (x – 2) and (x + 1) are factors of x³ + 3x² + ax + b, calculating the values of a and b and hence find the remaining factor.

Solutions:

Ques No 14

Given that (x + 2) and (x – 3) are factors of x³ + ax + b, calculate the values of a and b and hence find the remaining factor.

Solutions:

Ques No 15

Factorize, using remainder theorem:

(i) x³ – 19x – 30

(ii) x³ + 7x² – 21x – 27

(iii) x³ – 3x² – 9x – 5

(iv) 2x³ + 9x² + 7x – 6

Solutions 15(i):

Solutions 15(ii):

Solutions 15(iii):

Solutions 15(iv):

Ques No 16

(x – 3) is HCF of x³ – 2x² + px + 6 and x² – 5x + q. Find (6p + 9q).

Solutions:

ICSE Maths Solutions Class 10 Chapter 7 Factor Theorem Factorization: Ques No 17

(i) What number must be subtracted from x³ – 6x² – 15x + 80 so that the result is exactly divisible by (x + 4).

(i) What number must be added to x³ – 3x² – 12x + 19 so that the result is exactly divisible by (x – 2).

S Chand ICSE Math Class 10 Solutions 17(i):

Solutions 17(ii):