Factor polynomial $$ 2x^{2}+38x+70 $$

$$ 2x^{2}+38x+70 = 2( x^{2}+19x+35 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 2x^{2}+38x+70 = 2 ( x^{2}+19x+35 ) $$

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:

$$ \color{blue}{ b = 19 } ~ \text{ and } ~ \color{red}{ c = 35 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 19 } $ and multiply to $ \color{red}{ 35 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 35 }$.

PRODUCT = 35
1     35	-1     -35
5     7	-5     -7

Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ 19 }$, we conclude the polynomial cannot be factored.

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