It seems that $ x^{2}-2600x+240000 $ cannot be factored out.
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:
$$ \color{blue}{ b = -2600 } ~ \text{ and } ~ \color{red}{ c = 240000 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -2600 } $ and multiply to $ \color{red}{ 240000 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 240000 }$.
| PRODUCT = 240000 | |
| 1 240000 | -1 -240000 |
| 2 120000 | -2 -120000 |
| 3 80000 | -3 -80000 |
| 4 60000 | -4 -60000 |
| 5 48000 | -5 -48000 |
| 6 40000 | -6 -40000 |
| 8 30000 | -8 -30000 |
| 10 24000 | -10 -24000 |
| 12 20000 | -12 -20000 |
| 15 16000 | -15 -16000 |
| 16 15000 | -16 -15000 |
| 20 12000 | -20 -12000 |
| 24 10000 | -24 -10000 |
| 25 9600 | -25 -9600 |
| 30 8000 | -30 -8000 |
| 32 7500 | -32 -7500 |
| 40 6000 | -40 -6000 |
| 48 5000 | -48 -5000 |
| 50 4800 | -50 -4800 |
| 60 4000 | -60 -4000 |
| 64 3750 | -64 -3750 |
| 75 3200 | -75 -3200 |
| 80 3000 | -80 -3000 |
| 96 2500 | -96 -2500 |
| 100 2400 | -100 -2400 |
| 120 2000 | -120 -2000 |
| 125 1920 | -125 -1920 |
| 128 1875 | -128 -1875 |
| 150 1600 | -150 -1600 |
| 160 1500 | -160 -1500 |
| 192 1250 | -192 -1250 |
| 200 1200 | -200 -1200 |
| 240 1000 | -240 -1000 |
| 250 960 | -250 -960 |
| 300 800 | -300 -800 |
| 320 750 | -320 -750 |
| 375 640 | -375 -640 |
| 384 625 | -384 -625 |
| 400 600 | -400 -600 |
| 480 500 | -480 -500 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -2600 }$, we conclude the polynomial cannot be factored.