Factor polynomial $$ 2x^{2}+10x-100 $$

$$ 2x^{2}+10x-100 = 2( x-5 )( x+10 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 2x^{2}+10x-100 = 2 ( x^{2}+5x-50 ) $$

Step 2 :

Step 2: 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:

$$ \color{blue}{ b = 5 } ~ \text{ and } ~ \color{red}{ c = -50 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 5 } $ and multiply to $ \color{red}{ -50 } $.

Step 3: 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 4: Find out which pair sums up to $\color{blue}{ b = 5 }$

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

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

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

Polynomial Factoring Calculator