Factor polynomial $$ 6x^{2}-37x-35 $$

$$ 6x^{2}-37x-35 = ( x-7 )( 6x+5 ) $$

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:

$$ a = 6 , b = -37 ~ \text{ and } ~ c = -35 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 6 }$ by the constant term $\color{blue}{c = -35} $.

$$ a \cdot c = -210 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -210 $ and add to $ b = -37 $.

Step 4: All pairs of numbers with a product of $ -210 $ are:

PRODUCT = -210
-1     210	1     -210
-2     105	2     -105
-3     70	3     -70
-5     42	5     -42
-6     35	6     -35
-7     30	7     -30
-10     21	10     -21
-14     15	14     -15

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -37 }$

PRODUCT = -210 and SUM = -37
-1     210	1     -210
-2     105	2     -105
-3     70	3     -70
-5     42	5     -42
-6     35	6     -35
-7     30	7     -30
-10     21	10     -21
-14     15	14     -15

Step 6: Replace middle term $ -37 x $ with $ 5x-42x $:

$$ 6x^{2}-37x-35 = 6x^{2}+5x-42x-35 $$

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

$$ 6x^{2}+5x-42x-35 = x\left(6x+5\right) -7\left(6x+5\right) = \left(x-7\right) \left(6x+5\right) $$

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