Factor polynomial $$ x^{2}-40x+4800 $$
Answer
It seems that $ x^{2}-40x+4800 $ 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:
$$ \color{blue}{ b = -40 } ~ \text{ and } ~ \color{red}{ c = 4800 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -40 } $ and multiply to $ \color{red}{ 4800 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 4800 }$.
| PRODUCT = 4800 | |
| 1 4800 | -1 -4800 |
| 2 2400 | -2 -2400 |
| 3 1600 | -3 -1600 |
| 4 1200 | -4 -1200 |
| 5 960 | -5 -960 |
| 6 800 | -6 -800 |
| 8 600 | -8 -600 |
| 10 480 | -10 -480 |
| 12 400 | -12 -400 |
| 15 320 | -15 -320 |
| 16 300 | -16 -300 |
| 20 240 | -20 -240 |
| 24 200 | -24 -200 |
| 25 192 | -25 -192 |
| 30 160 | -30 -160 |
| 32 150 | -32 -150 |
| 40 120 | -40 -120 |
| 48 100 | -48 -100 |
| 50 96 | -50 -96 |
| 60 80 | -60 -80 |
| 64 75 | -64 -75 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -40 }$, we conclude the polynomial cannot be factored.
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