Factor polynomial $$ -2x^{2}+26x-44 $$

$$ -2x^{2}+26x-44 = ( -2 )( x-2 )( x-11 ) $$

Step 1 :

After factoring out $ -2 $ we have:

$$ -2x^{2}+26x-44 = -2 ( x^{2}-13x+22 ) $$

Step 2 :

Step 2: Identify constants $ \color{blue}{ b }$ and $\color{red}{ c }$. ( $ \color{blue}{ b }$ is a number in front of the $ x $ term and $ \color{red}{ c } $ is a constant). In our case:

$$ \color{blue}{ b = -13 } ~ \text{ and } ~ \color{red}{ c = 22 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -13 } $ and multiply to $ \color{red}{ 22 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 22 }$.

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

Step 4: Find out which pair sums up to $\color{blue}{ b = -13 }$

PRODUCT = 22 and SUM = -13
1     22	-1     -22
2     11	-2     -11

Step 5: Put -2 and -11 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-13x+22 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-13x+22 & = (x -2)(x -11) \end{aligned} $$

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