Factor polynomial $$ 4x^{2}-4x-22 $$

$$ 4x^{2}-4x-22 = 2( 2x^{2}-2x-11 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 4x^{2}-4x-22 = 2 ( 2x^{2}-2x-11 ) $$

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:

$$ a = 2 , b = -2 ~ \text{ and } ~ c = -11 $$

Step 3: Multiply the leading coefficient $\color{blue}{ a = 2 }$ by the constant term $\color{blue}{c = -11} $.

$$ a \cdot c = -22 $$

Step 4: Find out two numbers that multiply to $ a \cdot c = -22 $ and add to $ b = -2 $.

Step 5: All pairs of numbers with a product of $ -22 $ are:

PRODUCT = -22
-1     22	1     -22
-2     11	2     -11

Step 6: Find out which factor pair sums up to $\color{blue}{ b = -2 }$

Step 7: Because none of these pairs will give us a sum of $ \color{blue}{ -2 }$, we conclude the polynomial cannot be factored.

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