Factor polynomial $$ x^{2}+4x-60 $$

$$ x^{2}+4x-60 = ( x-6 )( x+10 ) $$

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:

$$ \color{blue}{ b = 4 } ~ \text{ and } ~ \color{red}{ c = -60 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 4 } $ and multiply to $ \color{red}{ -60 } $.

Step 2: Find out pairs of numbers with a product of $\color{red}{ c = -60 }$.

PRODUCT = -60
-1     60	1     -60
-2     30	2     -30
-3     20	3     -20
-4     15	4     -15
-5     12	5     -12
-6     10	6     -10

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

PRODUCT = -60 and SUM = 4
-1     60	1     -60
-2     30	2     -30
-3     20	3     -20
-4     15	4     -15
-5     12	5     -12
-6     10	6     -10

Step 4: Put -6 and 10 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+4x-60 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+4x-60 & = (x -6)(x + 10) \end{aligned} $$

Polynomial Factoring Calculator