The answer is D.
Explanation:
You can find the zeroes of a polynomial function in factored form by setting each factor equal to zero and solve for [tex]x[/tex].
The polynomial function of answer A is not even factored, so we can rule that one out.
Lets set each one of the factors of answer B equal to zero, solve for [tex]x[/tex] and see what happens:
- [tex]x=0[/tex]
- [tex]x-3=0[/tex]
[tex]x=3[/tex]
- [tex]x+4=0[/tex]
[tex]x=-4[/tex]
As you can see, our zeroes are 0,3, and -4, so this is not the correct answer either.
The polynomial function of answer C is not even factored, so we can rule that one out as well.
Lets apply what we just learned to the factored polynomial of answer D:
- [tex]x=0[/tex]
- [tex]x+3=0[/tex]
[tex]x=-3[/tex]
- [tex]x-4=0[/tex]
[tex]x=4[/tex]
This time our zeroes are, 0, -3, and 4; therefore we can conclude that D is the correct answer.
