It seems that $ x^{2}+2x-42 $ 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:
$$ \color{blue}{ b = 2 } ~ \text{ and } ~ \color{red}{ c = -42 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 2 } $ and multiply to $ \color{red}{ -42 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -42 }$.
| PRODUCT = -42 | |
| -1 42 | 1 -42 |
| -2 21 | 2 -21 |
| -3 14 | 3 -14 |
| -6 7 | 6 -7 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ 2 }$, we conclude the polynomial cannot be factored.