Factorize:
$(i) x^{2} + 9 x + 18$
$(i i) 6 x^{2} + 7 x - 3$
$(i i i) 2 x^{2} - 7 x - 15$
$(i v) 84 - 2 r - 2 r^{2}$

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Solution

$(i) .$
$x^{2} + 9 x + 18 = x^{2} + 3 x + 6 x + 18$
$= x (x + 3) + 6 (x + 3)$
$= (x + 3) (x + 6)$

$(i i) .$
$6 x^{2} + 7 x - 3 = 6 x^{2} + 9 x - 2 x - 3$
$= 3 x (2 x + 3) - 1 (2 x + 3)$
$= (3 x - 1) (2 x + 3)$

$(i i i) .$
$2 x^{2} - 7 x - 15 = 2 x^{2} - 10 x + 3 x - 15$
$= 2 x (x - 5) + 3 (x - 5)$
$= (x - 5) (2 x + 3)$

$(i v) .$
$84 - 2 r - 2 r^{2} = - (2 r^{2} + 2 r - 84)$
$= - (2 r^{2} + 14 r + 12 r - 84)$
$= - (2 r (r + 7) - 12 (r + 7))$
$= - (r + 7) (2 r - 12)$

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x^{2} + 9 x + 18

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