SOLUTION: Consider the following f(x)=x^5+x^3-6x a. Find all the real zeros of the polynomial function. b. Determine the end behavior of the polymial.

Question 1135039: Consider the following f(x)=x^5+x^3-6x
a. Find all the real zeros of the polynomial function.
b. Determine the end behavior of the polymial.
Answer by swincher4391(1107) (Show Source): You can put this solution on YOUR website!
Factor.
There's an x in common with every one of those terms so we can definitely factor out x.
x(x^4 + x^2 - 6)
Think of this as:
x((x^2)^2 + (x)^2 - 6)
Let's take care of the easy one first. When x is a factor, this would just mean that x = 0. But since the polynomial has degree 5, we must check to make sure there aren't others (up to a maximum of 5).
So by any quadratic factoring/solving method you want to use, you should get to this result:
x^2 = (-1 +- sqrt(1^2 - (-24)))/2
x^2 = -3 or 2
Clearly x^2 = -3 does not yield any real zeroes, so look at x^2 = 2. While not a perfect square, this still has two answers. Those are +-sqrt(2).
b) The degree is 5, hence this function has odd behavior. The leading coefficient is greater than 0, so we know the end behavior is that of any positive odd function, namely from the left it is decreasing and from the right, it is increasing.

RELATED QUESTIONS
Consider the following f(x)=x^5+x^3-6x a. Find all the real zeros of the polynomial... (answered by solver91311)

Consider the following f(x)=x^5+x^3-6x a. Find all the real zeros of the polynomial... (answered by ikleyn)

Consider the polynomial function f(x)=x^4-x^3-x^2-x-2 a) How many zeros does f(x)... (answered by Fombitz)

Consider the following. f(x)=1/2x^2+3/2x-1/2 (a) Find all the real zeros of... (answered by ReadingBoosters)

Given the following polynomial,find a).the zeros and the multiplicity of each b).where... (answered by stanbon)

how do i find the end behavior of the polynomial function?... (answered by josgarithmetic)

Find all real zeros of the function.... (answered by robertb)

Find all real zeros of the function.... (answered by Edwin McCravy)

For the polynomial Function : F(x)=-2(x + 1/2) (x+4)^3 a)List each real zero and its... (answered by MathLover1,Boreal)