Factor polynomial $$ x^{2}+x-90 $$

$$ x^{2}+x-90 = ( x-9 )( x+10 ) $$

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:

$$ \color{blue}{ b = 1 } ~ \text{ and } ~ \color{red}{ c = -90 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 1 } $ and multiply to $ \color{red}{ -90 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -90 }$.

PRODUCT = -90
-1     90	1     -90
-2     45	2     -45
-3     30	3     -30
-5     18	5     -18
-6     15	6     -15
-9     10	9     -10

Step 3: Find out which pair sums up to $\color{blue}{ b = 1 }$

PRODUCT = -90 and SUM = 1
-1     90	1     -90
-2     45	2     -45
-3     30	3     -30
-5     18	5     -18
-6     15	6     -15
-9     10	9     -10

Step 4: Put -9 and 10 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+x-90 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+x-90 & = (x -9)(x + 10) \end{aligned} $$

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