Step 1 :
After factoring out $ x $ we have:
$$ x^{3}+x^{2}+3x = x ( x^{2}+x+3 ) $$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:
$$ \color{blue}{ b = 1 } ~ \text{ and } ~ \color{red}{ c = 3 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 1 } $ and multiply to $ \color{red}{ 3 } $.
Step 3: Find out pairs of numbers with a product of $\color{red}{ c = 3 }$.
PRODUCT = 3 | |
1 3 | -1 -3 |
Step 4: Because none of these pairs will give us a sum of $ \color{blue}{ 1 }$, we conclude the polynomial cannot be factored.