Question
Factor polynomial $$ x^{2}-124x+100 $$
Answer
It seems that $ x^{2}-124x+100 $ cannot be factored out.
Explanation
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:
$$ \color{blue}{ b = -124 } ~ \text{ and } ~ \color{red}{ c = 100 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -124 } $ and multiply to $ \color{red}{ 100 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 100 }$.
| PRODUCT = 100 | |
| 1 100 | -1 -100 |
| 2 50 | -2 -50 |
| 4 25 | -4 -25 |
| 5 20 | -5 -20 |
| 10 10 | -10 -10 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -124 }$, we conclude the polynomial cannot be factored.
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