Factor polynomial $$ t^{2}+4t-5 $$

$$ t^{2}+4t-5 = ( t-1 )( t+5 ) $$

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:

$$ \color{blue}{ b = 4 } ~ \text{ and } ~ \color{red}{ c = -5 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 4 } $ and multiply to $ \color{red}{ -5 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -5 }$.

PRODUCT = -5
-1     5	1     -5

Step 3: Find out which pair sums up to $\color{blue}{ b = 4 }$

PRODUCT = -5 and SUM = 4
-1     5	1     -5

Step 4: Put -1 and 5 into placeholders to get factored form.

$$ \begin{aligned} t^{2}+4t-5 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ t^{2}+4t-5 & = (x -1)(x + 5) \end{aligned} $$

Polynomial Factoring Calculator