Question

Solve 2a^2 - 24a +54 by splitting the middle term

Answer 1

Answer:

(a - 9) (a - 6)

Step-by-step explanation: 2a² - 24a + 54

= 2a² - 18a - 6a + 54

[since -18 + (-6) = -24 and -18 × (-6) = 2 × 54 = 108]

= 2a(a - 9) - 6(a - 9) [taking out common factors]

= (a - 9) ( a - 6) [ grouping the terms]

Answer 2

$2 {a}^{2} - 24a + 54$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 54 = - 16 \times - 8 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 24 = - 16 - 8$

$2 {a}^{2} - 8a - 16a + 54 \\ 2 a(a - 4) - 16(a - 4) \\ (2a - 16)(a - 4) = 0 \\ 2a - 16 = 0 \: or \: a - 4 = 0$

$a = \frac{16}{2} or \: a = 4$