Find the zeros of the polynomial function.

f(x) = x3 + 4x2 - 9x - 36

Question

Find the zeros of the polynomial function.

f(x) = x3 + 4x2 - 9x - 36

tkhunny · Answer

Where do you suppose one should start?

anonymous · Answer

that's the problem I duno....    :/

tkhunny · Answer

That is not an acceptable answer.  You MUST have SOME idea.  Seriously, why do you have this problem to solve?  Did you study any of these things listed below?

DesCartes Rule of Signs?
Rational Root Theorem?
Fixed Point Iteration?
Newton's Method?

tkhunny · Answer

Factoring?
Grouping?
Quadratic Formula?
Completing the Square?

Let me know when I hit something with which you are familiar.

tkhunny · Answer

This one factors nicely by grouping.  I don't actually recommend "grouping" as a primary method of factoring, but sometimes it just pops out.

$f(x) = x^{3} + 4x^{2} - 9x - 36$

$f(x) = x^{2}(x+4) - 9(x + 4)$

$f(x) = (x^{2}-9)(x+4)$

And, we're almost done.