Factor polynomial $$ -x^{2}+4x+3 $$

It seems that $ -x^{2}+4x+3 $ cannot be factored out.

Step 1 :

After factoring out $ -1 $ we have:

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:

Now we must discover two numbers that sum up to $ \color{blue}{ -4 } $ and multiply to $ \color{red}{ -3 } $.

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

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