• 100% Satisfaction Guarantee
ExcelSpecialist,
Category: Math Homework
Satisfied Customers: 368
33656705
Type Your Math Homework Question Here...
ExcelSpecialist is online now

# 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

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