Factor polynomial $$ m^{2}-63m+486 $$

$$ m^{2}-63m+486 = ( m-9 )( m-54 ) $$

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:

$$ \color{blue}{ b = -63 } ~ \text{ and } ~ \color{red}{ c = 486 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -63 } $ and multiply to $ \color{red}{ 486 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 486 }$.

PRODUCT = 486
1     486	-1     -486
2     243	-2     -243
3     162	-3     -162
6     81	-6     -81
9     54	-9     -54
18     27	-18     -27

Step 3: Find out which pair sums up to $\color{blue}{ b = -63 }$

PRODUCT = 486 and SUM = -63
1     486	-1     -486
2     243	-2     -243
3     162	-3     -162
6     81	-6     -81
9     54	-9     -54
18     27	-18     -27

Step 4: Put -9 and -54 into placeholders to get factored form.

$$ \begin{aligned} m^{2}-63m+486 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ m^{2}-63m+486 & = (x -9)(x -54) \end{aligned} $$

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