Question
Factor polynomial $$ y^{2}-35y+324 $$
Answer
It seems that $ y^{2}-35y+324 $ 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:
$$ \color{blue}{ b = -35 } ~ \text{ and } ~ \color{red}{ c = 324 }$$Now we must discover two numbers that sum up to $ \color{blue}{ -35 } $ and multiply to $ \color{red}{ 324 } $.
Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 324 }$.
| PRODUCT = 324 | |
| 1 324 | -1 -324 |
| 2 162 | -2 -162 |
| 3 108 | -3 -108 |
| 4 81 | -4 -81 |
| 6 54 | -6 -54 |
| 9 36 | -9 -36 |
| 12 27 | -12 -27 |
| 18 18 | -18 -18 |
Step 3: Because none of these pairs will give us a sum of $ \color{blue}{ -35 }$, we conclude the polynomial cannot be factored.
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