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