Factorize each of the following expressions : (Q. 1-8)1. x2 + 7x + 122. x2

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Step-by-step explanation:

$1) \: \: {x}^{2} + 7x + 12 \\ \: \: \: = {x}^{2} + 3x + 4x + 12 \\ \: \: \: = x(x + 3) + 4(x + 3) \\ \: \: \: = (x + 4)(x + 3) \\ \\ 2) \: \: {x}^{2} - 14x + 48 \\ \: \: \: = {x}^{2} - 6x - 8x + 48 \\ \: \: \: = x(x - 6) - 8(x - 6) \\ \: \: \: = (x - 8)(x - 6) \\ \\ 3) \: \: {x}^{2} - 7x - 18 \\ \: \: \: = {x}^{2} - 9x + 2x - 18 \\ \: \: \: = x(x - 9) + 2(x - 9) \\ \: \: \: = (x + 2)(x - 9) \\ \\ 4) \: \: {x}^{2} - 25x + 84 \\ \: \: \: = {x}^{2} - 21x - 4x + 84 \\ \: \: \: = x(x - 21) - 4(x - 21) \\ \: \: \: = (x - 4)(x - 21)$

$5) \: \: 2 {x}^{2} + 7x + 6 \\ \: \: \: = 2 {x}^{2} + 3x + 4x + 6 \\ \: \: \: = x(2x + 3) + 2(2x + 3) \\ \: \: \: = (x + 2)(2x + 3) \\ \\ 6) \: \: 2 {x}^{2} - 13x + 15 \\ \: \: \: = 2 { {x}^{2} } - 10x - 3x + 15 \\ \: \: \: = 2x(x - 5) - 3(x - 5) \\ \: \: \: = (2x - 3)(x - 5) \\ \\ 7) \: \: 3 {x}^{2} - 14x + 8 \\ \: \: \: = 3 {x}^{2} - 12x - 2x + 8 \\ \: \: \: = 3x(x - 4) - 2(x - 4) \\ \: \: \: = (3x - 2)(x - 4) \\ \\ 8) \: \: 3 {x}^{2} + 10x - 8 \\ \: \: \: = 3 {x}^{2} + 12x - 2x - 8 \\ \: \: \: = 3x(x + 4) - 2(x + 4) \\ \: \: \: = (3x - 2)(x + 4)$

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Solution :-

3→ x² - 7x - 18

By splitting middle term

→ x² - 9x + 2x - 18

→ x ( x - 9 ) +2 ( x - 9 )

→ ( x + 2 ) ( x - 9 )

Therefore ( x + 2 ) ( x - 9 ) is the correct answer

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