Question
Factor polynomial $$ x^{2}-x-984064 $$
Answer
It seems that $ x^{2}-x-984064 $ 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:
$$ \color{blue}{ b = -1 } ~ \text{ and } ~ \color{red}{ c = -984064 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -1 } $ and multiply to $ \color{red}{ -984064 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -984064 }$.
| PRODUCT = -984064 | |
| -1 984064 | 1 -984064 |
| -2 492032 | 2 -492032 |
| -4 246016 | 4 -246016 |
| -8 123008 | 8 -123008 |
| -16 61504 | 16 -61504 |
| -31 31744 | 31 -31744 |
| -32 30752 | 32 -30752 |
| -62 15872 | 62 -15872 |
| -64 15376 | 64 -15376 |
| -124 7936 | 124 -7936 |
| -128 7688 | 128 -7688 |
| -248 3968 | 248 -3968 |
| -256 3844 | 256 -3844 |
| -496 1984 | 496 -1984 |
| -512 1922 | 512 -1922 |
| -961 1024 | 961 -1024 |
| -992 992 | 992 -992 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -1 }$, we conclude the polynomial cannot be factored.
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