Question
Factor polynomial $$ m^{2}+13m-36 $$
Answer
It seems that $ m^{2}+13m-36 $ 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:
$$ \color{blue}{ b = 13 } ~ \text{ and } ~ \color{red}{ c = -36 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 13 } $ and multiply to $ \color{red}{ -36 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -36 }$.
| PRODUCT = -36 | |
| -1 36 | 1 -36 |
| -2 18 | 2 -18 |
| -3 12 | 3 -12 |
| -4 9 | 4 -9 |
| -6 6 | 6 -6 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ 13 }$, we conclude the polynomial cannot be factored.
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