Factor polynomial $$ 18x^{2}+6x-4 $$

$$ 18x^{2}+6x-4 = 2( 3x-1 )( 3x+2 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 18x^{2}+6x-4 = 2 ( 9x^{2}+3x-2 ) $$

Step 2 :

Step 2: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 9 , b = 3 ~ \text{ and } ~ c = -2 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = -2} $.

$$ a \cdot c = -18 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -18 $ and add to $ b = 3 $.

Step 5: All pairs of numbers with a product of $ -18 $ are:

PRODUCT = -18
-1     18	1     -18
-2     9	2     -9
-3     6	3     -6

Step 6: Find out which factor pair sums up to $\color{blue}{ b = 3 }$

PRODUCT = -18 and SUM = 3
-1     18	1     -18
-2     9	2     -9
-3     6	3     -6

Step 7: Replace middle term $ 3 x $ with $ 6x-3x $:

$$ 9x^{2}+3x-2 = 9x^{2}+6x-3x-2 $$

Step 8: Apply factoring by grouping. Factor $ 3x $ out of the first two terms and $ -1 $ out of the last two terms.

$$ 9x^{2}+6x-3x-2 = 3x\left(3x+2\right) -1\left(3x+2\right) = \left(3x-1\right) \left(3x+2\right) $$

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