Question
Factor polynomial $$ x^{2}-12x+144 $$
Answer
It seems that $ x^{2}-12x+144 $ 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:
$$ \color{blue}{ b = -12 } ~ \text{ and } ~ \color{red}{ c = 144 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -12 } $ and multiply to $ \color{red}{ 144 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 144 }$.
| PRODUCT = 144 | |
| 1 144 | -1 -144 |
| 2 72 | -2 -72 |
| 3 48 | -3 -48 |
| 4 36 | -4 -36 |
| 6 24 | -6 -24 |
| 8 18 | -8 -18 |
| 9 16 | -9 -16 |
| 12 12 | -12 -12 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -12 }$, we conclude the polynomial cannot be factored.
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