How do you factor $18x^2 -15x - 18$ ?

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Answer 1 · 2017-02-12T00:15:52

$18x^2-15x-18 = 3(3x+2)(2x-3)$

First separate out the common scalar factor $3$ , then use an AC method...

$18x^2-15x-18 = 3(6x^2-5x-6)$

To factor $6x^2-5x-6$ first look for a pair of factors of $AC = 6*6 = 36$ which differ by $B=5$ .

The pair $9, 4$ works.

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

$6x^2-5x-6 = (6x^2-9x)+(4x-6)$

$color(white)(6x^2-5x-6) = 3x(2x-3)+2(2x-3)$

$color(white)(6x^2-5x-6) = (3x+2)(2x-3)$

Putting it all together:

$18x^2-15x-18 = 3(3x+2)(2x-3)$

How do you factor 18x^2 -15x - 1818x^2 -15x - 18?