## ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 6 Factorization Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 6 Factorization Chapter Test

Question 1.

Find the remainder when 2x^{3} – 3x^{2} + 4x + 7 is divided by

(i) x – 2

(ii) x + 3

(iii) 2x + 1

Solution:

Question 2.

When 2x^{3} – 9x^{2} + 10x – p is divided by (x + 1), the remainder is -24.Find the value of p.

Solution:

Question 3.

If (2x – 3) is a factor of 6x^{2} + x + a, find the value of a. With this value of a, factorize the given expression.

Solution:

Question 4.

When 3x^{2} – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x^{2} – 5x + p – 3.

Solution:

Question 5.

Prove that (5x + 4) is a factor of 5x^{3} + 4x^{2} – 5x – 4. Hence factorize the given polynomial completely.

Solution:

Question 6.

Use factor theorem to factorise the following polynomials completely:

(i) 4x^{3} + 4x^{2} – 9x – 9

(ii) x^{3} – 19x – 30

Solution:

Question 7.

If x^{3} – 2x^{2} + px + q has a factor (x + 2) and leaves a remainder 9, when divided by (x + 1), find the values of p and q. With these values of p and q, factorize the given polynomial completely.

Solution:

Question 8.

If (x + 3) and (x – 4) are factors of x^{3} + ax^{2} – bx + 24, find the values of a and b: With these values of a and b, factorize the given expression.

Solution:

Question 9.

If 2x^{3} + ax^{2} – 11x + b leaves remainder 0 and 42 when divided by (x – 2) and (x – 3) respectively, find the values of a and b. With these values of a and b, factorize the given expression.

Solution:

Question 10.

If (2x + 1) is a factor of both the expressions 2x^{2} – 5x + p and 2x^{2} + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.

Solution:

Question 11.

When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).

Solution: