Factor polynomial $$ -a^{2}-a+72 $$

$$ -a^{2}-a+72 = -( a-8 )( a+9 ) $$

Step 1 :

After factoring out $ -1 $ we have:

$$ -a^{2}-a+72 = - ~ ( a^{2}+a-72 ) $$

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:

$$ \color{blue}{ b = 1 } ~ \text{ and } ~ \color{red}{ c = -72 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 1 } $ and multiply to $ \color{red}{ -72 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -72 }$.

PRODUCT = -72
-1     72	1     -72
-2     36	2     -36
-3     24	3     -24
-4     18	4     -18
-6     12	6     -12
-8     9	8     -9

Step 4: Find out which pair sums up to $\color{blue}{ b = 1 }$

PRODUCT = -72 and SUM = 1
-1     72	1     -72
-2     36	2     -36
-3     24	3     -24
-4     18	4     -18
-6     12	6     -12
-8     9	8     -9

Step 5: Put -8 and 9 into placeholders to get factored form.

$$ \begin{aligned} a^{2}+a-72 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ a^{2}+a-72 & = (x -8)(x + 9) \end{aligned} $$

Polynomial Factoring Calculator