Question
Factor polynomial $$ x^{2}+14x+240 $$
Answer
It seems that $ x^{2}+14x+240 $ 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:
$$ \color{blue}{ b = 14 } ~ \text{ and } ~ \color{red}{ c = 240 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 14 } $ and multiply to $ \color{red}{ 240 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 240 }$.
| PRODUCT = 240 | |
| 1 240 | -1 -240 |
| 2 120 | -2 -120 |
| 3 80 | -3 -80 |
| 4 60 | -4 -60 |
| 5 48 | -5 -48 |
| 6 40 | -6 -40 |
| 8 30 | -8 -30 |
| 10 24 | -10 -24 |
| 12 20 | -12 -20 |
| 15 16 | -15 -16 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ 14 }$, we conclude the polynomial cannot be factored.
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