Factor polynomial $$ x^{2}-16x-360 $$
Answer
It seems that $ x^{2}-16x-360 $ 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:
$$ \color{blue}{ b = -16 } ~ \text{ and } ~ \color{red}{ c = -360 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -16 } $ and multiply to $ \color{red}{ -360 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -360 }$.
| PRODUCT = -360 | |
| -1 360 | 1 -360 |
| -2 180 | 2 -180 |
| -3 120 | 3 -120 |
| -4 90 | 4 -90 |
| -5 72 | 5 -72 |
| -6 60 | 6 -60 |
| -8 45 | 8 -45 |
| -9 40 | 9 -40 |
| -10 36 | 10 -36 |
| -12 30 | 12 -30 |
| -15 24 | 15 -24 |
| -18 20 | 18 -20 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -16 }$, we conclude the polynomial cannot be factored.
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