Factor polynomial $$ 7x^{2}-26x-8 $$

$$ 7x^{2}-26x-8 = ( x-4 )( 7x+2 ) $$

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:

$$ a = 7 , b = -26 ~ \text{ and } ~ c = -8 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 7 }$ by the constant term $\color{blue}{c = -8} $.

$$ a \cdot c = -56 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -56 $ and add to $ b = -26 $.

Step 4: All pairs of numbers with a product of $ -56 $ are:

PRODUCT = -56
-1     56	1     -56
-2     28	2     -28
-4     14	4     -14
-7     8	7     -8

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -26 }$

PRODUCT = -56 and SUM = -26
-1     56	1     -56
-2     28	2     -28
-4     14	4     -14
-7     8	7     -8

Step 6: Replace middle term $ -26 x $ with $ 2x-28x $:

$$ 7x^{2}-26x-8 = 7x^{2}+2x-28x-8 $$

Step 7: Apply factoring by grouping. Factor $ x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 7x^{2}+2x-28x-8 = x\left(7x+2\right) -4\left(7x+2\right) = \left(x-4\right) \left(7x+2\right) $$

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