Answer:
A. [tex]f(x)=(x+6)(x-2)[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2+4x-12[/tex]
To rewrite the equation such that the zeros of the function can be easily identified.
Solution:
In order to find the zeros of the given quadratic function, we will use factorization by splitting up the middle term.
We have:
[tex]f(x)=x^2+4x-12[/tex]
Splitting [tex]4x[/tex] into two term such that the sum of the two terms = [tex]4x[/tex](middle term) and the product of the two terms is =[tex]-12x^2[/tex] (product of first and last term)
The terms are [tex]6x,-2x[/tex] as their sum = [tex]4x[/tex] and their product = [tex]-12x^2[/tex]
So, we have:
[tex]f(x)=x^2+6x-2x-12[/tex]
Factoring in pairs of first two terms and last two terms by factoring out their G.C.F.
[tex]f(x)=x(x+6)-2(x+6)[/tex]
Since [tex](x+6)[/tex] is a common term, we can factor it out further.
[tex]f(x)=(x+6)(x-2)[/tex] (Answer)
From the above function, we can identify that the zeros of the function are -6 and 2.
