Factor polynomial $$ y^{2}-12y+20 $$

$$ y^{2}-12y+20 = ( y-2 )( y-10 ) $$

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:

$$ \color{blue}{ b = -12 } ~ \text{ and } ~ \color{red}{ c = 20 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -12 } $ and multiply to $ \color{red}{ 20 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = 20 }$.

PRODUCT = 20
1     20	-1     -20
2     10	-2     -10
4     5	-4     -5

Step 3: Find out which pair sums up to $\color{blue}{ b = -12 }$

PRODUCT = 20 and SUM = -12
1     20	-1     -20
2     10	-2     -10
4     5	-4     -5

Step 4: Put -2 and -10 into placeholders to get factored form.

$$ \begin{aligned} y^{2}-12y+20 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ y^{2}-12y+20 & = (x -2)(x -10) \end{aligned} $$

Polynomial Factoring Calculator