Factor polynomial $$ 2x^{2}-7x-30 $$

$$ 2x^{2}-7x-30 = ( x-6 )( 2x+5 ) $$

Step 1: 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:

$$ a = 2 , b = -7 ~ \text{ and } ~ c = -30 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -30} $.

$$ a \cdot c = -60 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -60 $ and add to $ b = -7 $.

Step 4: All pairs of numbers with a product of $ -60 $ are:

PRODUCT = -60
-1     60	1     -60
-2     30	2     -30
-3     20	3     -20
-4     15	4     -15
-5     12	5     -12
-6     10	6     -10

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -7 }$

PRODUCT = -60 and SUM = -7
-1     60	1     -60
-2     30	2     -30
-3     20	3     -20
-4     15	4     -15
-5     12	5     -12
-6     10	6     -10

Step 6: Replace middle term $ -7 x $ with $ 5x-12x $:

$$ 2x^{2}-7x-30 = 2x^{2}+5x-12x-30 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -6 $ out of the last two terms.

$$ 2x^{2}+5x-12x-30 = x\left(2x+5\right) -6\left(2x+5\right) = \left(x-6\right) \left(2x+5\right) $$

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