Question
Factor polynomial $$ x^{2}-305x+750 $$
Answer
It seems that $ x^{2}-305x+750 $ 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:
$$ \color{blue}{ b = -305 } ~ \text{ and } ~ \color{red}{ c = 750 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -305 } $ and multiply to $ \color{red}{ 750 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 750 }$.
| PRODUCT = 750 | |
| 1 750 | -1 -750 |
| 2 375 | -2 -375 |
| 3 250 | -3 -250 |
| 5 150 | -5 -150 |
| 6 125 | -6 -125 |
| 10 75 | -10 -75 |
| 15 50 | -15 -50 |
| 25 30 | -25 -30 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -305 }$, we conclude the polynomial cannot be factored.
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