It seems that $ 9x^{2}-x-576 $ cannot be factored out.
Step 1: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:
Step 2: Multiply the leading coefficient $\color{blue}{ a = 9 }$ by the constant term $\color{blue}{c = -576} $.
$$ a \cdot c = -5184 $$Step 3: Find out two numbers that multiply to $ a \cdot c = -5184 $ and add to $ b = -1 $.
Step 4: All pairs of numbers with a product of $ -5184 $ are:
| PRODUCT = -5184 | |
| -1 5184 | 1 -5184 |
| -2 2592 | 2 -2592 |
| -3 1728 | 3 -1728 |
| -4 1296 | 4 -1296 |
| -6 864 | 6 -864 |
| -8 648 | 8 -648 |
| -9 576 | 9 -576 |
| -12 432 | 12 -432 |
| -16 324 | 16 -324 |
| -18 288 | 18 -288 |
| -24 216 | 24 -216 |
| -27 192 | 27 -192 |
| -32 162 | 32 -162 |
| -36 144 | 36 -144 |
| -48 108 | 48 -108 |
| -54 96 | 54 -96 |
| -64 81 | 64 -81 |
| -72 72 | 72 -72 |
Step 5: Find out which factor pair sums up to $\color{blue}{ b = -1 }$
Step 6: Because none of these pairs will give us a sum of $ \color{blue}{ -1 }$, we conclude the polynomial cannot be factored.