Question
Factor polynomial $$ x^{2}+4x-420 $$
Answer
It seems that $ x^{2}+4x-420 $ 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:
$$ \color{blue}{ b = 4 } ~ \text{ and } ~ \color{red}{ c = -420 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 4 } $ and multiply to $ \color{red}{ -420 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -420 }$.
| PRODUCT = -420 | |
| -1 420 | 1 -420 |
| -2 210 | 2 -210 |
| -3 140 | 3 -140 |
| -4 105 | 4 -105 |
| -5 84 | 5 -84 |
| -6 70 | 6 -70 |
| -7 60 | 7 -60 |
| -10 42 | 10 -42 |
| -12 35 | 12 -35 |
| -14 30 | 14 -30 |
| -15 28 | 15 -28 |
| -20 21 | 20 -21 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ 4 }$, we conclude the polynomial cannot be factored.
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