How JustAnswer Works:
  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site.
    Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.
Ask ExcelSpecialist Your Own Question
ExcelSpecialist
ExcelSpecialist,
Category: Math Homework
Satisfied Customers: 368
33656705
Type Your Math Homework Question Here...
ExcelSpecialist is online now
A new question is answered every 9 seconds

How can I factor completely P(x) X^6+16X^3+64 find all zeros

Customer Question

How can I factor completely P(x)=X^6+16X^3+64
find all zeros state multiplicity
Real zero
Complex complex
Submitted: 5 years ago.
Category: Math Homework
Expert:  ExcelSpecialist replied 5 years ago.

Hello,

 

If you re-write P(x) = X^6 + 16X³ + 64 as P(x) = (X³)² + 2*8X³ + 8² you can see that P(X) = (X³ + 8)²

 

This way you find that there is only 1 (real) zero X = -2 with multiplicity 6 (since the sum of multiplicities must be equal to the degree of the polynomial).

 

 

Let me know if you have any further questions.

 

Best regards,

 

Tom

ExcelSpecialist and other Math Homework Specialists are ready to help you
Customer: replied 5 years ago.
Ok now we have (X^3+8)^2
How can you find the zeros of (X^3+8) I have only reduced to a linear factor and a irreducible quadratic. Never saw this type of problem with a X^3 before.
Customer: replied 5 years ago.
Ok I understand
Expert:  ExcelSpecialist replied 5 years ago.

Well, you can find the zeros of (X³+8)² by finding the values for which (X³+8)² = 0

 

So:

(X³+8)² = 0

--> X³+8 = 0

--> X³ = -8

--> X = ³√(-8) = -2 (since you know that (-2) * (-2) * (-2) = -8)

 

Best regards,

 

Tom

ExcelSpecialist and other Math Homework Specialists are ready to help you
Customer: replied 5 years ago.
How do you right the complex zeros
Expert:  ExcelSpecialist replied 5 years ago.

In this example there aren't any complex zeros.

 

Best regards,

 

Tom