It seems that $ x^{2}-6x+368 $ cannot be factored out.
Step 1: 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:
$$ \color{blue}{ b = -6 } ~ \text{ and } ~ \color{red}{ c = 368 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -6 } $ and multiply to $ \color{red}{ 368 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 368 }$.
PRODUCT = 368 | |
1 368 | -1 -368 |
2 184 | -2 -184 |
4 92 | -4 -92 |
8 46 | -8 -46 |
16 23 | -16 -23 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -6 }$, we conclude the polynomial cannot be factored.