Factor polynomial $$ 2p^{2}-48p-50 $$

$$ 2p^{2}-48p-50 = 2( p+1 )( p-25 ) $$

Step 1 :

After factoring out $ 2 $ we have:

$$ 2p^{2}-48p-50 = 2 ( p^{2}-24p-25 ) $$

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:

$$ \color{blue}{ b = -24 } ~ \text{ and } ~ \color{red}{ c = -25 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ -24 } $ and multiply to $ \color{red}{ -25 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -25 }$.

PRODUCT = -25
-1     25	1     -25
-5     5	5     -5

Step 4: Find out which pair sums up to $\color{blue}{ b = -24 }$

PRODUCT = -25 and SUM = -24
-1     25	1     -25
-5     5	5     -5

Step 5: Put 1 and -25 into placeholders to get factored form.

$$ \begin{aligned} p^{2}-24p-25 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ p^{2}-24p-25 & = (x + 1)(x -25) \end{aligned} $$

Polynomial Factoring Calculator