It seems that $ 8x^{2}+215x+32 $ 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 $\color{blue}{ a = 8 }$ by the constant term $\color{blue}{c = 32} $.
$$ a \cdot c = 256 $$Step 3: Find out two numbers that multiply to $ a \cdot c = 256 $ and add to $ b = 215 $.
Step 4: All pairs of numbers with a product of $ 256 $ are:
| PRODUCT = 256 | |
| 1 256 | -1 -256 |
| 2 128 | -2 -128 |
| 4 64 | -4 -64 |
| 8 32 | -8 -32 |
| 16 16 | -16 -16 |
Step 5: Find out which factor pair sums up to $\color{blue}{ b = 215 }$
Step 6: Because none of these pairs will give us a sum of $ \color{blue}{ 215 }$, we conclude the polynomial cannot be factored.