SOLUTION: Factor the Polynomial completely p(x)= x^5+6x^3+9x Find all its zeros. State the multiplicity of each zero. Im specifically not understanding how to fund multiplicity, so

Question 1099282: Factor the Polynomial completely
p(x)= x^5+6x^3+9x
Find all its zeros. State the multiplicity of each zero.
Im specifically not understanding how to fund multiplicity, so please dont forget that part.
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
.
Factor the Polynomial completely
p(x)= x^5+6x^3+9x
~~~~~~~~~~~~~~~~~~~~

 =  =    


     ! Notice that x^4 + 6x^2 + 9 =  = .  
       Therefore, you can continue this chain of equalities in this way


=  =


      The only real zero is z= 0.  All other zeroes are complex zeroes.
      So, you can continue in the complex domain


= .


      Now you can see that there is one real zero x= 0 of multiplicity 1,

                                        complex zero x= 3i of multiplicity 2, and

                                        complex zero  x= -3i of multiplicity 2.

RELATED QUESTIONS
Factor the polynomial completely. P(x) = 625x4 − 16 Find all its zeros. State the (answered by josgarithmetic)

Hi! Factor the polynomial completely. P (x) = x^6 + 2x^3 + 1 Find all zeros and (answered by RAY100)

Factor the polynomial completely, and find all its zeros. State the multiplicity of each (answered by oscargut)

Factor the polynomial completely. P(x) = x3 + 25x Find all its zeros. State the... (answered by Fombitz)

Factor the polynomial completely. {{{Q(x) = x^2 + 4x + 5}}} Find all its zeros. State (answered by josgarithmetic)

A) Factor the Polynomial Completely P(x)= x^3 - 3x^2 + 4x B) Find all its zeros.... (answered by Fombitz,Boreal)

A) Factor the Polynomial Completely P(x)= 81x^4 -625 B) Find all its zeros. State... (answered by Boreal)

Find the zeros of the polynomial function below and state the multiplicity of each zero. (answered by Tatiana_Stebko)

Find the zeros of the polynomial function below and state the multiplicity of each zero. (answered by stanbon)