# How do you factor 24x ^ { 3} + 60x ^ { 2} - 168x - 420?

Jun 22, 2017

$\left(12 {x}^{2} - 84\right) \left(2 x + 5\right)$

#### Explanation:

$24 {x}^{3} + 60 {x}^{2} - 168 x - 420$

What we can do is break it up into:

$24 {x}^{3} + 60 {x}^{2}$ & $- 168 x - 420$

We will factor this by grouping, find the GCF for each of them:

The GCF for $24 {x}^{3} + 60 {x}^{2}$ is $\textcolor{b l u e}{12 {x}^{2}}$

The GCF for $- 168 x - 420$ is $\textcolor{b l u e}{- 42}$

Now let's factor them:

$24 {x}^{3} + 60 {x}^{2} \to \textcolor{b l u e}{12 {x}^{2}} \left(2 x + 5\right)$
$- 168 x - 420 \to \textcolor{b l u e}{- 84} \left(2 x + 5\right)$

We can see that $\textcolor{b l u e}{12 {x}^{2}} \textcolor{b l u e}{- 84}$ is one factor the other one is $2 x + 5$

Our final answer is $\left(12 {x}^{2} - 84\right) \left(2 x + 5\right)$

Jun 22, 2017

$2 \left(2 x + 5\right) \left(2 {x}^{2} - 7\right)$

#### Explanation:

$f \left(x\right) = 12 \left(2 {x}^{3} + 5 {x}^{2} - 14 x - 35\right) = 12 y$
$F a c \to r y b y g r o u \pi n g :$
$y = 2 {x}^{2} \left(x + 5\right) - 7 \left(2 x + 5\right) = \left(2 x + 5\right) \left(2 {x}^{2} - 7\right)$
f$\left(x\right) = 12 \left(2 x + 5\right) \left(2 {x}^{2} - 7\right)$