Factor polynomial $$ x^{2}-15x+50 $$

$$ x^{2}-15x+50 = ( x-5 )( x-10 ) $$

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:

$$ \color{blue}{ b = -15 } ~ \text{ and } ~ \color{red}{ c = 50 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -15 } $ and multiply to $ \color{red}{ 50 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 50 }$.

PRODUCT = 50
1     50	-1     -50
2     25	-2     -25
5     10	-5     -10

Step 3: Find out which pair sums up to $\color{blue}{ b = -15 }$

PRODUCT = 50 and SUM = -15
1     50	-1     -50
2     25	-2     -25
5     10	-5     -10

Step 4: Put -5 and -10 into placeholders to get factored form.

$$ \begin{aligned} x^{2}-15x+50 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}-15x+50 & = (x -5)(x -10) \end{aligned} $$

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