Factor polynomial $$ y^{2}-45y+324 $$

$$ y^{2}-45y+324 = ( y-9 )( y-36 ) $$

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:

$$ \color{blue}{ b = -45 } ~ \text{ and } ~ \color{red}{ c = 324 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -45 } $ 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: Find out which pair sums up to $\color{blue}{ b = -45 }$

PRODUCT = 324 and SUM = -45
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 4: Put -9 and -36 into placeholders to get factored form.

$$ \begin{aligned} y^{2}-45y+324 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ y^{2}-45y+324 & = (x -9)(x -36) \end{aligned} $$

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