Factorization Class 10 ICSE ML Aggarwal Chapter Test

ML Aggarwal Class 10 Solutions Factorization Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test.

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Question 1.
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by
(i) x – 2
(ii) x + 3
(iii) 2x + 1
Solution:
f(x) = 2x3 – 3x2 + 4x + 7
(i) Let x – 2 = 0, then x = 2
Substituting value of x in f(x)
f(2) = 2 (2)3 – 3 (2)2 + 4 (2) + 7
= 2 × 8 – 3 × 4 + 4 × 2 + 7
= 16 – 12 + 8 + 7 = 19
Remainder = 19 Ans.
(ii) Let x + 3 = 0, then x = – 3
Substituting the value of x in f(x)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q1.1

Question 2.
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
Solution:
Let x + 1 = 0 then x = – 1,
Substituting the value of x in f(x)
f(x) = 2x3 – 9x2 + 10x – p
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q2.1

Question 3.
If (2x – 3) is a factor of 6x2 + x + a, find the value of a. With this value of a, factorise the given expression.
Solution:
Let 2 x – 3 = 0 then 2x = 3
=>x = \(\\ \frac { 3 }{ 2 } \)
Substituting the value of x in f(x)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q3.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q3.2

Question 4.
When 3x2 – 5x + p is divided by (x – 2), the remainder is 3. Find the value of p. Also factorise the polynomial 3x2 – 5x + p – 3.
Solution:
f(x) = 3x2 – 5x+ p
Let (x – 2) = 0, then x = 2
f(2) = 3 (2)2 – 5(2) + p
= 3 x 4 – 10 + p
= 12 – 10 + p
= 2 + p
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q4.1

Question 5.
Prove that (5x + 4) is a factor of 5x3 + 4x2 – 5x – 4. Hence factorise the given polynomial completely.
Solution:
f(x) = 5x3 + 4x2 – 5x – 4
Let 5x + 4 = 0, then 5x = – 4
=> x = \(\\ \frac { -4 }{ 2 } \)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q5.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q5.2

Question 6.
Use factor theorem to factorise the following polynomials completely:
(i) 4x3 + 4x2 – 9x – 9
(ii) x3 – 19x – 30
Solution:
(i) f(x) = 4x3 + 4x2 – 9x – 9
Let x = – 1,then
f( – 1) = 4 ( – 1)3 + 4 ( – 1)2 – 9 ( – 1) – 9
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q6.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q6.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q6.3

Question 7.
If x3 – 2x2 + 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, factorise the given polynomial completely.
Solution:
f(x) = x3 – 2x2 + px + q
(x + 2) is a factor
f( – 2) = ( – 2)3 – 2( – 2)2 + p ( – 2) + q
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q7.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q7.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q7.3

Question 8.
If (x + 3) and (x – 4) are factors of x3 + ax2 – bx + 24, find the values of a and b: With these values of a and b, factorise the given expression.
Solution:
f(x) = x3 + ax2 – bx + 24
Let x + 3 = 0, then x = – 3
Substituting the value of x in f(x)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q8.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q8.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q8.3

Question 9.
If 2x3 + ax2 – 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, factorise the given expression.
Solution:
f(x) = 2x3 + ax2 – 11 x + b
Let x – 2 = 0, then x = 2,
Substituting the vaue of x in f(x)
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q9.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q9.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q9.3

Question 10.
If (2x + 1) is a factor of both the expressions 2x2 – 5x + p and 2x2 + 5x + q, find the value of p and q. Hence find the other factors of both the polynomials.
Solution:
Let 2x + 1 = 0, then 2x = – 1
x = \(– \frac { 1 }{ 2 } \)
Substituting the value of x in
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q10.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q10.2
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q10.3

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:
When f(x) is divided by (x – 1),
Remainder = 5
Let r – 1 = 0 => x = 1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q11.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test Q11.2

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 7 Factorization Chapter Test are helpful to complete your math homework.

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