Factor polynomial $$ 5x^{2}-100x+120 $$

$$ 5x^{2}-100x+120 = 5( x^{2}-20x+24 ) $$

Step 1 :

After factoring out $ 5 $ we have:

$$ 5x^{2}-100x+120 = 5 ( x^{2}-20x+24 ) $$

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:

$$ \color{blue}{ b = -20 } ~ \text{ and } ~ \color{red}{ c = 24 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -20 } $ and multiply to $ \color{red}{ 24 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 24 }$.

PRODUCT = 24
1     24	-1     -24
2     12	-2     -12
3     8	-3     -8
4     6	-4     -6

Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ -20 }$, we conclude the polynomial cannot be factored.

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