Step 1 :
After factoring out $ 2 $ we have:
$$ 2x^{2}+10x-72 = 2 ( x^{2}+5x-36 ) $$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:
$$ \color{blue}{ b = 5 } ~ \text{ and } ~ \color{red}{ c = -36 }$$Now we must discover two numbers that sum up to $ \color{blue}{ 5 } $ and multiply to $ \color{red}{ -36 } $.
Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -36 }$.
PRODUCT = -36 | |
-1 36 | 1 -36 |
-2 18 | 2 -18 |
-3 12 | 3 -12 |
-4 9 | 4 -9 |
-6 6 | 6 -6 |
Step 4: Find out which pair sums up to $\color{blue}{ b = 5 }$
PRODUCT = -36 and SUM = 5 | |
-1 36 | 1 -36 |
-2 18 | 2 -18 |
-3 12 | 3 -12 |
-4 9 | 4 -9 |
-6 6 | 6 -6 |
Step 5: Put -4 and 9 into placeholders to get factored form.
$$ \begin{aligned} x^{2}+5x-36 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+5x-36 & = (x -4)(x + 9) \end{aligned} $$