# How do you find all the zeros of #f(x)=x^3+3x^2-4x-12#?

##### 2 Answers

Factor by grouping to find zeros:

#### Explanation:

Notice that the ratio between the first and second terms is the same as that between the third and fourth terms.

So this cubic factors by grouping:

#x^3+3x^2-4x-12#

#=(x^3+3x^2)-(4x+12)#

#=x^2(x+3)-4(x+3)#

#=(x^2-4)(x+3)#

#=(x-2)(x+2)(x+3)#

Hence zeros:

#### Explanation:

We essentially have two parts to our function:

Let's factor a

Since both terms have an

You might immediately recognize that what I have in red is a difference of squares, which can be factored as

We now have

Hope this helps!