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