Factor polynomial $$ 4x^{3}+28x^{2}-72x $$

$$ 4x^{3}+28x^{2}-72x = 4x( x-2 )( x+9 ) $$

Step 1 :

After factoring out $ 4x $ we have:

$$ 4x^{3}+28x^{2}-72x = 4x ( x^{2}+7x-18 ) $$

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:

$$ \color{blue}{ b = 7 } ~ \text{ and } ~ \color{red}{ c = -18 }$$

Now we must discover two numbers that sum up to $ \color{blue}{ 7 } $ and multiply to $ \color{red}{ -18 } $.

Step 3: Find out pairs of numbers with a product of $\color{red}{ c = -18 }$.

PRODUCT = -18
-1     18	1     -18
-2     9	2     -9
-3     6	3     -6

Step 4: Find out which pair sums up to $\color{blue}{ b = 7 }$

PRODUCT = -18 and SUM = 7
-1     18	1     -18
-2     9	2     -9
-3     6	3     -6

Step 5: Put -2 and 9 into placeholders to get factored form.

$$ \begin{aligned} x^{2}+7x-18 & = (x + \color{orangered}{\square} )(x + \color{orangered}{\square}) \\ x^{2}+7x-18 & = (x -2)(x + 9) \end{aligned} $$

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