Factor polynomial $$ t^{2}+6t-27 $$

$$ t^{2}+6t-27 = ( t-3 )( t+9 ) $$

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:

$$ \color{blue}{ b = 6 } ~ \text{ and } ~ \color{red}{ c = -27 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 6 } $ and multiply to $ \color{red}{ -27 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -27 }$.

PRODUCT = -27
-1     27	1     -27
-3     9	3     -9

Step 3: Find out which pair sums up to $\color{blue}{ b = 6 }$

PRODUCT = -27 and SUM = 6
-1     27	1     -27
-3     9	3     -9

Step 4: Put -3 and 9 into placeholders to get factored form.

$$ \begin{aligned} t^{2}+6t-27 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ t^{2}+6t-27 & = (x -3)(x + 9) \end{aligned} $$

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