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

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Answer 1 · 2017-06-22T01:26:09

$(12x^2-84)(2x+5)$

Let's start with what we got:

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

What we can do is break it up into:

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

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

The GCF for $24x^3+60x^2$ is $color(blue)(12x^2)$

The GCF for $-168x-420$ is $color(blue)(-42)$

Now let's factor them:

$24x^3+60x^2->color(blue)(12x^2)(2x+5)$
$-168x-420->color(blue)(-84)(2x+5)$

We can see that $color(blue)(12x^2)color(blue)(-84)$ is one factor the other one is $2x+5$

Our final answer is $(12x^2-84)(2x+5)$

Answer 2 · 2017-06-22T05:07:41

$2(2x + 5)(2x^2 - 7)$

$f(x) = 12(2x^3 + 5x^2 - 14x - 35) = 12y$
$Factor y by grouping:$
$y = 2x^2(x + 5) - 7(2x + 5) = (2x + 5)(2x^2 - 7)$
f $(x) = 12(2x + 5)(2x^2 - 7)$

How do you factor 24x ^ { 3} + 60x ^ { 2} - 168x - 42024x ^ { 3} + 60x ^ { 2} - 168x - 420?