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Question 23Fa...

Question

Question 23
Factorise
(i) $x^{2} + 9 x + 18$
(ii) $6 x^{2} + 7 x - 3$
(iii) $2 x^{2} - 7 x - 15$
(iv) $84 - 2 r - 2 r^{2}$

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Solution

(i) $x^{2} + 9 x + 18 = x^{2} + 6 x + 3 x + 18$ [By splitting the middle term]
$= x (x + 6) + 3 (x + 6) = (x + 3) (x + 6)$

(ii) $6 x^{2} + 7 x - 3 = 6 x^{2} + 9 x - 2 x - 3$ [By splitting the middle term]
$= 3 x (2 x + 3) - 1 (2 x + 3) = (3 x - 1) (2 x + 3)$

(iii) $2 x^{2} - 7 x - 15 = 2 x^{2} - 10 x + 3 x - 15$ [By splitting the middle term]
$= 2 x (x - 5) + 3 (x - 5) = (2 x + 3) (x - 5)$

(iv) $84 - 2 r - 2 r^{2} = - 2 (r^{2} + r - 42)$
$= - 2 (r^{2} + 7 r - 6 r - 42)$ [By splitting the middle term]
$= - 2 [r (r + 7) - 6 (r + 7_{)}]$
$= - 2 (r - 6) (r + 7) = 2 (6 - r) (r + 7)$

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Similar questions

x^{2} + 9 x + 18

6 x^{2} + 7 x - 3

2 x^{2} - 7 x - 15

84 - 2 r - 2 r^{2}

12 x^{2} - 7 x + 1

2 x^{2} + 7 x + 3

6 x^{2} + 5 x - 6

3 x^{2} - x - 4

Factorise:
(i) $12 x^{2} - 7 x + 1$
(ii) $2 x^{2} + 7 x + 3$
(iii) $6 x^{2} + 5 x - 6$
(iv) $3 x^{2} - x - 4$

(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}

\frac{3 x^{2} - x - 2}{x^{2} - 7 x + 12} \div \frac{3 x^{2} - 7 x - 6}{x^{2} - 4}

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