myhelper: RS Aggarwal solution class 8 chapter 7 Factorisation Exercise 7D

Exercise 7D

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Q1 | Ex-7D | Class 8 | RS AGGARWAL | Factorisation | Chapter 7 | myhelper

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Question 1:

Factorise:
x² + 5x + 6

Answer 1:

$T h e g i v e n e x p r e s s i o n i s x^{2} + 5 x + 6 . Find two numbers that follow the conditions given below : S u m = 5 P r o d u c t = 6 C l e a r l y, t h e n u m b e r s a r e 3 a n d 2 . x^{2} + 5 x + 6 = x^{2} + 3 x + 2 x + 6 = x (x + 3) + 2 (x + 3) = (x + 3) (x + 2)$

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Question 2:

Factorise:
y² + 10y + 24

Answer 2:

$T h e g i v e n e x p r e s s i o n i s y^{2} + 10 y + 24 . Find two numbers that follow the conditions given below : S u m = 10 P r o d u c t = 24 C l e a r l y, t h e n u m b e r s a r e 6 a n d 4 . y^{2} + 10 y + 24 = y^{2} + 6 y + 4 y + 24 = y (y + 6) + 4 (y + 6) = (y + 6) (y + 4)$

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Question 3:

Factorise:
z² + 12z + 27

Answer 3:

$T h e g i v e n e x p r e s s i o n i s z^{2} + 12 z + 27 . Find two numbers that follow the conditions given below : S u m = 12 P r o d u c t = 27 C l e a r l y, t h e n u m b e r s a r e 9 a n d 3 . z^{2} + 12 z + 27 = z^{2} + 9 z + 3 z + 27 = z (z + 9) + 3 (z + 9) = (z + 9) (z + 3)$

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Question 4:

Factorise:
p² + 6p + 8

Answer 4:

$T h e g i v e n e x p r e s s i o n i s p^{2} + 6 p + 8 . Find two numbers that follow the conditions given below : S u m = 6 P r o d u c t = 8 C l e a r l y, t h e n u m b e r s a r e 4 a n d 2 . p^{2} + 6 p + 8 = p^{2} + 4 p + 2 p + 8 = p (p + 4) + 2 (p + 4) = (p + 4) (p + 2)$

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Question 5:

Factorise:
x² + 15x + 56

Answer 5:

$T h e g i v e n e x p r e s s i o n i s x^{2} + 15 x + 56 . Find two numbers that follow the conditions given below : S u m = 15 P r o d u c t = 56 C l e a r l y, t h e n u m b e r s a r e 8 a n d 7 . x^{2} + 15 x + 56 = x^{2} + 8 x + 7 x + 56 = x (x + 8) + 7 (x + 8) = (x + 8) (x + 7)$

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Question 6:

Factorise:
y² + 19y + 60

Answer 6:

$T h e g i v e n e x p r e s s i o n i s y^{2} + 19 y + 60 . Find two numbers that follow the conditions given below : S u m = 19 P r o d u c t = 60 C l e a r l y, t h e n u m b e r s a r e 15 a n d 4 . y^{2} + 19 y + 60 = y^{2} + 15 y + 4 y + 60 = y (y + 15) + 4 (y + 15) = (y + 15) (y + 4)$

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Question 7:

Factorise:
x² + 13x + 40

Answer 7:

$T h e g i v e n e x p r e s s i o n i s x^{2} + 13 x + 40 . Find two numbers that follow the conditions given below : S u m = 13 P r o d u c t = 40 C l e a r l y, t h e n u m b e r s a r e 8 a n d 5 . x^{2} + 13 x + 40 = x^{2} + 8 x + 5 x + 40 = x (x + 8) + 5 (x + 8) = (x + 8) (x + 5)$

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Question 8:

Factorise:
q² − 10q + 21

Answer 8:

$T h e g i v e n e x p r e s s i o n i s q^{2} - 10 q + 21 . Find two numbers that follow the conditions given below : S u m = - 10 P r o d u c t = 21 C l e a r l y, t h e n u m b e r s a r e - 7 a n d - 3 . q^{2} - 10 q + 21 = q^{2} - 7 q - 3 q + 21 = q (q - 7) - 3 (q - 7) = (q - 7) (q - 3)$

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Question 9:

Factorise:
p² + 6p − 16

Answer 9:

$T h e g i v e n e x p r e s s i o n i s p^{2} + 6 p - 16 . Find two numbers that follow the conditions given below : S u m = 6 P r o d u c t = - 16 C l e a r l y, t h e n u m b e r s a r e 8 a n d - 2 . p^{2} + 6 p - 16 = p^{2} + 8 p - 2 p - 16 = p (p + 8) - 2 (p + 8) = (p + 8) (p - 2)$

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Question 10:

Factorise:
x² − 10x + 24

Answer 10:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 10 x + 24 . Find two numbers that follow the conditions given below : S u m = - 10 P r o d u c t = 24 C l e a r l y, t h e n u m b e r s a r e - 6 a n d - 4 . x^{2} - 10 x + 24 = x^{2} - 6 x - 4 x + 24 = x (x - 6) - 4 (x - 6) = (x - 6) (x - 4)$

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Question 11:

Factorise:
x² − 23x + 42

Answer 11:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 23 x + 42 . Find two numbers that follow the conditions given below : S u m = - 23 P r o d u c t = 42 C l e a r l y, t h e n u m b e r s a r e - 21 a n d - 2 . x^{2} - 23 x + 42 = x^{2} - 21 x - 2 x + 42 = x (x - 21) - 2 (x - 21) = (x - 21) (x - 2)$

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Question 12:

Factorise:
x² − 17x + 16

Answer 12:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 17 x + 16 . Find two numbers that follow the conditions given below : S u m = - 17 P r o d u c t = 16 C l e a r l y, t h e n u m b e r s a r e - 16 a n d - 1 . x^{2} - 17 x + 16 = x^{2} - 16 x - x + 16 = x (x - 16) - 1 (x - 16) = (x - 16) (x - 1)$

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Question 13:

Factorise:
y² − 21y + 90

Answer 13:

$T h e g i v e n e x p r e s s i o n i s y^{2} - 21 y + 90 . Find two numbers that follow the conditions given below : S u m = - 21 P r o d u c t = 90 C l e a r l y, t h e n u m b e r s a r e - 15 a n d - 6 . y^{2} - 21 y + 90 = y^{2} - 15 y - 6 y + 90 = y (y - 15) - 6 (y - 15) = (y - 15) (y - 6)$

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Question 14:

Factorise:
x² − 22x + 117

Answer 14:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 22 x + 117 . Find two numbers that follow the conditions given below : S u m = - 22 P r o d u c t = 117 C l e a r l y, t h e n u m b e r s a r e - 13 a n d - 9 . x^{2} - 22 x + 117 = x^{2} - 13 x - 9 x + 117 = x (x - 13) - 9 (x - 13) = (x - 13) (x - 9)$

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Question 15:

Factorise:
x² − 9x + 20

Answer 15:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 9 x + 20 . Find two numbers that follow the conditions given below : S u m = - 9 P r o d u c t = 20 C l e a r l y, t h e n u m b e r s a r e - 5 a n d - 4 . x^{2} - 9 x + 20 = x^{2} - 5 x - 4 x + 20 = x (x - 5) - 4 (x - 5) = (x - 5) (x - 4)$

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Question 16:

Factorise:
x² + x − 132

Answer 16:

$T h e g i v e n e x p r e s s i o n i s x^{2} + x - 132 . Find two numbers that follow the conditions given below : S u m = 1 a n d P r o d u c t = - 132 C l e a r l y, t h e n u m b e r s a r e 12 a n d - 11 . x^{2} + x - 132 = x^{2} + 12 x - 11 x - 132 = x (x + 12) - 11 (x + 12) = (x + 12) (x - 11)$

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Question 17:

Factorise:
x² + 5x − 104

Answer 17:

$T h e g i v e n e x p r e s s i o n i s x^{2} + 5 x - 104 . Find two numbers that follow the conditions given below : S u m = 5 P r o d u c t = - 104 C l e a r l y, t h e n u m b e r s a r e 13 a n d - 8 . x^{2} + 5 x - 104 = x^{2} + 13 x - 8 x - 104 = x (x + 13) - 8 (x + 13) = (x + 13) (x - 8)$

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Question 18:

Factorise:
y² + 7y − 144

Answer 18:

$T h e g i v e n e x p r e s s i o n i s y^{2} + 7 y - 144 . Find two numbers that follow the conditions given below : S u m = 7 P r o d u c t = - 144 C l e a r l y, t h e n u m b e r s a r e 16 a n d - 9 . y^{2} + 7 y - 144 = y^{2} + 16 y - 9 y - 144 = y (y + 16) - 9 (y + 16) = (y + 16) (y - 9)$

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Question 19:

Factorise:
z² + 19z − 150

Answer 19:

$T h e g i v e n e x p r e s s i o n i s z^{2} + 19 z - 150 . Find two numbers that follow the conditions given below : S u m = 19 P r o d u c t = - 150 C l e a r l y, t h e n u m b e r s a r e 25 a n d - 6 . z^{2} + 19 z - 150 = z^{2} + 25 z - 6 z - 150 = z (z + 25) - 6 (z + 25) = (z + 25) (z - 6)$

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Question 20:

Factorise:
y² + y − 72

Answer 20:

$T h e g i v e n e x p r e s s i o n i s y^{2} + y - 72 . Find two numbers that follow the conditions given below : S u m = 1 P r o d u c t = - 72 C l e a r l y, t h e n u m b e r s a r e 9 a n d - 8 . y^{2} + y - 72 = y^{2} + 9 y - 8 y - 72 = y (y + 9) - 8 (y + 9) = (y + 9) (y - 8)$

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Question 21:

Factorise:
a² + 6a − 91

Answer 21:

$T h e g i v e n e x p r e s s i o n i s a^{2} + 6 a - 91 . Find two numbers that follow the conditions given below : S u m = 6 P r o d u c t = - 91 C l e a r l y, t h e n u m b e r s a r e 13 a n d - 7 . a^{2} + 6 a - 91 = a^{2} + 13 a - 7 a - 91 = a (a + 13) - 7 (a + 13) = (a + 13) (a - 7)$

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Question 22:

Factorise:
p² − 4p − 77

Answer 22:

$T h e g i v e n e x p r e s s i o n i s p^{2} - 4 p - 77 . Find two numbers that follow the conditions given below : S u m = - 4 P r o d u c t = - 77 C l e a r l y, t h e n u m b e r s a r e - 11 a n d 7 . p^{2} - 4 p - 77 = p^{2} - 11 p + 7 p - 77 = p (p - 11) + 7 (p - 11) = (p - 11) (p + 7)$

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Question 23:

Factorise:
x² − 7x − 30

Answer 23:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 7 x - 30 . Find two numbers that follow the conditions given below : S u m = - 7 P r o d u c t = - 30 C l e a r l y, t h e n u m b e r s a r e - 10 a n d 3 . x^{2} - 7 x - 30 = x^{2} - 10 x + 3 x - 30 = x (x - 10) + 3 (x - 10) = (x - 10) (x + 3)$

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Question 24:

Factorise:
x² − 11x − 42

Answer 24:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 11 x - 42 . Find two numbers that follow the conditions given below : S u m = - 11 P r o d u c t = - 42 C l e a r l y, t h e n u m b e r s a r e - 14 a n d 3 . x^{2} - 11 x - 42 = x^{2} - 14 x + 3 x - 42 = x (x - 14) + 3 (x - 14) = (x - 14) (x + 3)$

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Question 25:

Factorise:
x² − 5x − 24

Answer 25:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 5 x - 24 . Find two numbers that follow the conditions given below : S u m = - 5 P r o d u c t = - 24 C l e a r l y, t h e n u m b e r s a r e - 8 a n d 3 . x^{2} - 5 x - 24 = x^{2} - 8 x + 3 x - 24 = x (x - 8) + 3 (x - 8) = (x - 8) (x + 3)$

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Question 26:

Factorise:
y² − 6y − 135

Answer 26:

$T h e g i v e n e x p r e s s i o n i s y^{2} - 6 y - 135 . Find two numbers that follow the conditions given below : S u m = - 6 P r o d u c t = - 135 C l e a r l y, t h e n u m b e r s a r e - 15 a n d 9 . y^{2} - 6 y - 135 = y^{2} - 15 y + 9 y - 135 = y (y - 15) + 9 (y - 15) = (y - 15) (y + 9)$

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Question 27:

Factorise:
z² − 12z − 45

Answer 27:

$T h e g i v e n e x p r e s s i o n i s z^{2} - 12 z - 45 . Find two numbers that follow the conditions given below : S u m = - 12 P r o d u c t = - 45 C l e a r l y, t h e n u m b e r s a r e - 15 a n d 3 . z^{2} - 12 z - 45 = z^{2} - 15 z + 3 z - 45 = z (z - 15) + 3 (z - 15) = (z - 15) (z + 3)^{}$

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Question 28:

Factorise:
x² − 4x − 12

Answer 28:

$T h e g i v e n e x p r e s s i o n i s x^{2} - 4 x - 12 . Find two numbers that follow the conditions given below : S u m = - 4 P r o d u c t = - 12 C l e a r l y, t h e n u m b e r s a r e - 6 a n d 2 . x^{2} - 4 x - 12 = x^{2} - 6 x + 2 x - 12 = x (x - 6) + 2 (x - 6) = (x - 6) (x + 2)^{}$

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Question 29:

Factorise:
3x² + 10x + 8

Answer 29:

$T h e g i v e n e x p r e s s i o n i s 3 x^{2} + 10 x + 8 . Find two numbers that follow the conditions given below : S u m = 10 P r o d u c t = 3 \times 8 = 24 C l e a r l y, t h e n u m b e r s a r e 6 a n d 4 . 3 x^{2} + 10 x + 8 = 3 x^{2} + 10 x + 8 = 3 x^{2} + 6 x + 4 x + 8 = 3 x (x + 2) + 4 (x + 2) = (x + 2) (3 x + 4)^{}$

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Question 30:

Factorise:
3y² + 14y + 8

Answer 30:

$T h e g i v e n e x p r e s s i o n i s 3 y^{2} + 14 y + 8 Find two numbers that follow the conditions given below : S u m = 14 P r o d u c t = 24 C l e a r l y, t h e n u m b e r s a r e 12 a n d 2 . 3 y^{2} + 14 y + 8 = 3 y^{2} + 12 y + 2 y + 8 = 3 y (y + 4) + 2 (y + 4) = (3 y + 2) (y + 4)^{}$

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Question 31:

Factorise:
3z² − 10z + 8

Answer 31:

$T h e g i v e n e x p r e s s i o n i s 3 z^{2} - 10 z + 8 . Find two numbers that follow the conditions given below : S u m = - 10 P r o d u c t = 3 \times 8 = 24 C l e a r l y, t h e n u m b e r s a r e - 6 a n d - 4 . 3 z^{2} - 10 z + 8 = 3 z^{2} - 6 z - 4 z + 8 = 3 z (z - 2) - 4 (z - 2) = (3 z - 4) (z - 2)$

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Question 32:

Factorise:
2x² + x − 45

Answer 32:

$T h e g i v e n e x p r e s s i o n i s 2 x^{2} + x - 45 . Find two numbers that follow the conditions given below : S u m = 1 P r o d u c t = - 45 \times 2 = - 90 C l e a r l y, t h e n u m b e r s a r e 10 a n d - 9 . 2 x^{2} + x - 45 = 2 x^{2} + 10 x - 9 x - 45 = 2 x (x + 5) - 9 (x + 5) = (2 x - 9) (x + 5)$

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Question 33:

Factorise:
6p² + 11p − 10

Answer 33:

$T h e g i v e n e x p r e s s i o n i s 6 p^{2} + 11 p - 10 . Find two numbers that follow the conditions given below : S u m = 11 P r o d u c t = 6 \times - 10 = - 60 C l e a r l y, t h e n u m b e r s a r e 15 a n d - 4 . 6 p^{2} + 11 p - 10 = 6 p^{2} + 15 p - 4 p - 10 = 3 p (2 p + 5) - 2 (2 p + 5) = (2 p + 5) (3 p - 2)$

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Question 34:

Factorise:
2x² − 17x − 30

Answer 34:

$T h e g i v e n e x p r e s s i o n i s 2 x^{2} - 17 x - 30 . Find two numbers that follow the conditions given below : S u m = - 17 P r o d u c t = - 30 \times 2 = - 60 C l e a r l y, t h e n u m b e r s a r e - 20 a n d 3 . 2 x^{2} - 17 x - 30 = 2 x^{2} - 20 x + 3 x - 30 = 2 x (x - 10) + 3 (x - 10) = (2 x + 3) (x - 10)$

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Question 35:

Factorise:
7y² − 19y − 6

Answer 35:

$T h e g i v e n e x p r e s s i o n i s 7 y^{2} - 19 y - 6 . Find two numbers that follow the conditions given below : S u m = - 19 P r o d u c t = 7 \times - 6 = - 42 C l e a r l y, t h e n u m b e r s a r e - 21 a n d 2 . 7 y^{2} - 19 y - 6 = 7 y^{2} - 21 y + 2 y - 6 = 7 y (y - 3) + 2 (y - 3) = (7 y + 2) (y - 3)$

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Question 36:

Factorise:
28 − 31x − 5x²

Answer 36:

$T h e g i v e n e x p r e s s i o n i s 28 - 31 x - 5 x^{2} . Find two numbers that follow the conditions given below : S u m = - 31 P r o d u c t = 28 \times - 5 = - 140 C l e a r l y, t h e n u m b e r s a r e - 35 a n d 4 . 28 - 31 x - 5 x^{2} = 28 + 4 x - 35 x - 5 x^{2} = 4 (x + 7) - 5 x (7 + x) = (x + 7) (4 - 5 x)$

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Question 37:

Factorise:
3 + 23z − 8z²

Answer 37:

$T h e g i v e n e x p r e s s i o n i s 3 + 23 z - 8 z^{2} . Find two numbers that follow the conditions given below : S u m = 23 P r o d u c t = 3 \times - 8 = - 24 C l e a r l y, t h e n u m b e r s a r e 24 a n d - 1 . 3 + 23 z - 8 z^{2} = 3 + 24 z - z - 8 z^{2} = 3 (1 + 8 z) - z (1 + 8 z) = (1 + 8 z) (3 - z)$

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Question 38:

Factorise:
6x² − 5x − 6

Answer 38:

$T h e g i v e n e x p r e s s i o n i s 6 x^{2} - 5 x - 6 . Find two numbers that follow the conditions given below : S u m = - 5 P r o d u c t = - 6 \times 6 = - 36 C l e a r l y, t h e n u m b e r s a r e - 9 a n d 4 . 6 x^{2} - 5 x - 6 = 6 x^{2} - 9 x + 4 x - 6 = 3 x (2 x - 3) + 2 (2 x - 3) = (2 x - 3) (3 x + 2)$

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Question 39:

Factorise:
3m² + 24m + 36

Answer 39:

$T h e g i v e n e x p r e s s i o n i s 3 m^{2} + 24 m + 36 . Find two numbers that follow the conditions given below : S u m = 24 P r o d u c t = 36 \times 3 = 108 C l e a r l y, t h e n u m b e r s a r e 18 a n d 6 . 3 m^{2} + 24 m + 36 = 3 m^{2} + 18 m + 6 m + 36 = 3 m (m + 6) + 6 (m + 6) = (3 m + 6) (m + 6) = 3 (m + 2) (m + 6)$

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Question 40:

Factorise:
4n² − 8n + 3

Answer 40:

$T h e g i v e n e x p r e s s i o n i s 4 n^{2} - 8 n + 3 . Find two numbers that follow the conditions given below : S u m = - 8 P r o d u c t = 4 \times 3 = 12 C l e a r l y, t h e n u m b e r s a r e - 6 a n d - 2 . 4 n^{2} - 8 n + 3 = 4 n^{2} - 2 n - 6 n + 3 = 2 n (2 n - 1) - 3 (2 n - 1) = (2 n - 1) (2 n - 3)$

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Question 41:

Factorise:
6x² − 17x − 3

Answer 41:

$T h e g i v e n e x p r e s s i o n i s 6 x^{2} - 17 x - 3 . Find two numbers that follow the conditions given below : S u m = - 17 P r o d u c t = 6 \times - 3 = - 18 C l e a r l y, t h e n u m b e r s a r e - 18 a n d 1 . 6 x^{2} - 17 x - 3 = 6 x^{2} - 18 x + x - 3 = 6 x (x - 3) + 1 (x - 3) = (6 x + 1) (x - 3)$

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Question 42:

Factorise:
7x² − 19x − 6

Answer 42:

$T h e g i v e n e x p r e s s i o n i s 7 x^{2} - 19 x - 6 . Find two numbers that follow the conditions given below : S u m = - 19 P r o d u c t = 7 \times - 6 = - 42 C l e a r l y, t h e n u m b e r s a r e - 21 a n d 2 . 7 x^{2} - 19 x - 6 = 7 x^{2} - 21 x + 2 x - 6 = 7 x (x - 3) + 2 (x - 3) = (7 x + 2) (x - 3)$