Factor polynomial $$ x^{2}-16x+63 $$

$$ x^{2}-16x+63 = ( x-7 )( x-9 ) $$

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:

$$ \color{blue}{ b = -16 } ~ \text{ and } ~ \color{red}{ c = 63 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -16 } $ and multiply to $ \color{red}{ 63 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 63 }$.

PRODUCT = 63
1     63	-1     -63
3     21	-3     -21
7     9	-7     -9

Step 3: Find out which pair sums up to $\color{blue}{ b = -16 }$

PRODUCT = 63 and SUM = -16
1     63	-1     -63
3     21	-3     -21
7     9	-7     -9

Step 4: Put -7 and -9 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-16x+63 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-16x+63 & = (x -7)(x -9) \end{aligned} $$

Polynomial Factoring Calculator