Question

factorise
$x {}^{2} + 9x + 18$
​

Answer 1

Answer:

${x}^{2} + 9x + 18$

${x}^{2} + 6x + 3x + 18$

$x(x + 6) + 3(x + 6)$

$(x + 3)(x + 6)$

$x = - 3 \: or - 6$

Answer 2

Solution:

We have,

x² + 9x + 18

We try to split 9 into two parts whose sum is 9 and products is 18.

Clearly, 6 + 3 = 9 and 6 × 3 = 18

∴ x² + 9x + 18 = x² + (6x + 3x) + 18

➨ x(x + 6) +3 (x + 6)

➨ (x + 6) (x + 3)

Hence,

x² + 9x + 18 = (x+6) (x + 3)

Extra Dose:

• (a + b)³ = a³ + b³ + 3ab (a+b)
• (a - b)³ = a³ - b³ - 3ab (a -b)
• ( a - b)² = a² + b² - 2ab
• (a + b)² = a² + b² + 2ab