Factor polynomial $$ 2x^{2}-13x-7 $$

$$ 2x^{2}-13x-7 = ( x-7 )( 2x+1 ) $$

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:

$$ a = 2 , b = -13 ~ \text{ and } ~ c = -7 $$

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

$$ a \cdot c = -14 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -14 $ and add to $ b = -13 $.

Step 4: All pairs of numbers with a product of $ -14 $ are:

PRODUCT = -14
-1     14	1     -14
-2     7	2     -7

Step 5: Find out which factor pair sums up to $\color{blue}{ b = -13 }$

PRODUCT = -14 and SUM = -13
-1     14	1     -14
-2     7	2     -7

Step 6: Replace middle term $ -13 x $ with $ x-14x $:

$$ 2x^{2}-13x-7 = 2x^{2}+x-14x-7 $$

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

$$ 2x^{2}+x-14x-7 = x\left(2x+1\right) -7\left(2x+1\right) = \left(x-7\right) \left(2x+1\right) $$

Polynomial Factoring Calculator