Factor polynomial $$ p^{3}-3p^{2}-16p+48 $$

$$ p^{3}-3p^{2}-16p+48 = ( p-4 )( p+4 )( p-3 ) $$

Step 1 :

To factor $ p^{3}-3p^{2}-16p+48 $ we can use factoring by grouping:

Group $ \color{blue}{ x^{3} }$ with $ \color{blue}{ -3x^{2} }$ and $ \color{red}{ -16x }$ with $ \color{red}{ 48 }$ then factor each group.

$$ \begin{aligned} p^{3}-3p^{2}-16p+48 = ( \color{blue}{ x^{3}-3x^{2} } ) + ( \color{red}{ -16x+48 }) &= \\ &= \color{blue}{ x^{2}( x-3 )} + \color{red}{ -16( x-3 ) } = \\ &= (x^{2}-16)(x-3) \end{aligned} $$

Step 2 :

Rewrite $ p^{2}-16 $ as:

$$ p^{2}-16 = (p)^2 - (4)^2 $$

Now we can apply the difference of squares formula.

$$ I^2 - II^2 = (I - II)(I + II) $$

After putting $ I = p $ and $ II = 4 $ , we have:

$$ p^{2}-16 = (p)^2 - (4)^2 = ( p-4 ) ( p+4 ) $$

Polynomial Factoring Calculator