NCERT Solutions for Class 8 Maths - Factorisation- 2

Exercise 14.3 

Question 1: Carry out the following divisions: 

Solution:
(i)

(ii)

(iii)

(iv)

(v)

Question 2: Divide the given polynomial by the given monomial: 

Solution:
(i)

(ii)

(iii)

(iv)

(v)

Question 3: Work out the following divisions:

Solution: 

Question 4:  Divide as directed: 

Answer 4:

Question 5: Factorize the expressions and divide them as directed: 

Solution: 

                                          = m - 16

Exercise

 14.4 

Question: Find and correct the errors in the following mathematical statements.
1. 4(x – 5) = 4x – 5
2. x(3x + 2) = 3x² + 2
3. 2x + 3y = 5xy
4. x + 2x + 3x = 5x
5. 5y + 2y + y – 7y = 0
6. 3x + 2x = 5x²
7. (2x)² + 4(2x) + 7 = 2x² + 8x + 7
8. (2x)² + 5x = 4x + 5x = 9x²
9. (3x + 2)² = 3x² + 6x + 4
10. Substituting x = – 3 in
(a) x² + 5x + 4 gives (–3)² + 5(–3) + 4 = 9 + 2 + 4 = 15
(b) x² – 5x + 4 gives (–3)² – 5(–3) + 4 = 9 – 15 + 4 = – 2
(c) x² + 5x + 4 gives (–3)² + 5(–3) = – 9 – 15 = – 24
11. (y – 3)² = y² – 9
12. (z + 5)² = z² + 25
13. (2a + 3b)(a – b) = 2a² – 3b²
14. (a + 4)(a + 2) = a² + 8
15. (a – 4)(a – 2) = a² – 8
   





Solution:
1. 4(x – 5) = 4x – 5
The given statement is incorrect.
The correct statement is:
4(x – 5) = 4x – 20                           (∵ 4 * 5 = 20)

2. x(3x + 2) = 3x2 + 2
It is an incorrect statement.
The correct statement is:
x(3x + 2) = 3x² + 2x

3. 2x + 3y = 5xy
It is an incorrect statement.
The correct statement is:
2x + 3y = 2x + 3y

4. x + 2x + 3x = 5x
∵ 1 + 2 + 3 = 5 is an incorrect statement.
∴ The correct statement is:
x + 2x + 3x = 6x

5. 5y + 2y + y – 7y = 0
It is an incorrect statement.
∵ 5y + 2y + y = 8y and 8y – 7y = y
∴ The correct statement is
5y + 2y + y – 7y = y

6. 3x + 2x = 5x²
It is an incorrect statement.
The correct statement is:
3x + 2x = 5x

7. (2x)² + 4(2x) + 7= 2x² + 8x + 7
∵ (2x)² = 4x²
∴ The given statement is incorrect.
The correct statement is:
(2x)² + 4(2x) + 7 = 4x² + 8x + 7

8. (2x)² + 5x = 4x + 5x = 9x, is an incorrect statement.
∵ (2x)² = 4x²
∴ The correct statement is:
(2x)² + 5x = 4x² + 5x

9. (3x + 2)²= 3x² + 6x + 4
The given statement is incorrect.
∵ (3x + 2)² = (3x)² + 2(3x)(2) + (2)²
                 = 9x² + 6x + 4
∴ The correct statement is:
  (3x + 2)² = 9x² + 12x + 4

10. (a) Incorrect statement.
∵ x² + 5x + 4 = (–3)² + 5(–3) + 4
                     = 9 – 15 + 4
                     = (9 + 4) – 15
                     = 13 – 15 = –2
Thus, the correct statement is:
x² + 5x + 4 = (–3)² + 5(–3) + 4
                  = 9 – 15 + 4 = –2
(b) We have
     x² – 5x + 4 = (–3)² – 5(–3) + 4
                       = 9 + 15 + 4
                       = 28
∴ The correct statement is
x² – 5x + 4 at x = –3 is
(–3)² – 5(–3) + 4 = 9 + 15 + 4 = 28
(c) ∵   x² + 5x at x = – 3 is
        (–3)² + 5(–3) = 9 – 15 = –6
∴ The correct statement is
 x2 + 5x at x = –3 is
(–3)2 + 5(–3) = 9 – 15 = –6

11. (y – 3)² = y² – 9
The given statement is incorrect.
∵             (y – 3)² = y² – 2(y)(3) + (3)² = y² – 6y + 9
The correct statement is
               (y – 3)² = y² – 6y + 9

12. (z + 5)² = z² + 25
The given statement is incorrect.
∵     (z + 5)² = z² + 2(z)(5) + (5)²
                    = z² + 10z + 25
∴ The correct statement is
       (z + 5)2 = z² + 10z + 25

13.  (2a + 3b)(a – b) = 2a² – 3b²
∵      (2a + 3b) (a – b) = a(2a + 3b) – b (2a – 3b)
                                   = 2a² + 3ab – 2ab – 3b²
                                   = 2a² + ab – 3b²
∴ The correct statement is
         (2a + 3b)(a – b) = 2a² + ab - 3b²

14.  (a + 4)(a + 2) = a² + 8
Since (a + 4) (a + 2) = a (a + 4) + 2 (a + 4)
                                 = a² + 4a + 2a + 8
                                 = a² + 6a + 8

15.  (b – 4)(a – 2) = a²– 8
Since (a – 4)(a – 2) = a(a – 2) – 4(a – 2)
                               = a² – 2a – 4a + 8
                               = a² – 6a + 8
∴ The correct statement is
          (a – 4)(a – 2) = a² – 6a + 8

It is an incorrect statement.
∵ The correct statement is