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!