How do you factor $2 a^{2} - 9 a - 18$ $2a^2-9a-18$ ?

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How do you factor $2 a^{2} - 9 a - 18$ $2a^2-9a-18$ ?

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Answer 1 · 2016-05-09T18:30:15

$2 a^{2} - 9 a - 18 = (2 a + 3) (a - 6)$ $2a^2-9a-18=(2a+3)(a-6)$

Explanation:

Use an AC method:

Find a pair of factors of $A C = 2 \cdot 18 = 36$ $AC=2*18 = 36$ which differ by $B = 9$ $B=9$ .

The pair $12, 3$ $12, 3$ works in that $12 - 3 = 9$ $12-3=9$ and $12 \cdot 3 = 36$ $12*3=36$

Use this pair to split the middle term and factor by grouping:

$2 a^{2} - 9 a - 18$ $2a^2-9a-18$

$= 2 a^{2} - 12 a + 3 a - 18$ $=2a^2-12a+3a-18$

$= (2 a^{2} - 12 a) + (3 a - 18)$ $=(2a^2-12a)+(3a-18)$

$= 2 a (a - 6) + 3 (a - 6)$ $=2a(a-6)+3(a-6)$

$= (2 a + 3) (a - 6)$ $=(2a+3)(a-6)$

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How do you factor $2 a^{2} - 9 a - 18$ $2a^2-9a-18$ ?

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