Question
Factor polynomial $$ x^{2}-20x+200 $$
Answer
It seems that $ x^{2}-20x+200 $ 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:
$$ \color{blue}{ b = -20 } ~ \text{ and } ~ \color{red}{ c = 200 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -20 } $ and multiply to $ \color{red}{ 200 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 200 }$.
| PRODUCT = 200 | |
| 1 200 | -1 -200 |
| 2 100 | -2 -100 |
| 4 50 | -4 -50 |
| 5 40 | -5 -40 |
| 8 25 | -8 -25 |
| 10 20 | -10 -20 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -20 }$, we conclude the polynomial cannot be factored.
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