SOLUTION: z^(4)-z^(2)-2z+2 Please could someone help me with the last part of this question. Write the following polynomial as products of linear factors: z^(4)-z^(2)-2z+2 My try s

Question 978698: z^(4)-z^(2)-2z+2
Please could someone help me with the last part of this question.
Write the following polynomial as products of linear factors:
z^(4)-z^(2)-2z+2
My try so far:
(z-1)(z^3+z^2-2)
(z-1)(z-1)(z^2+z+2)
From here I tried to use the quadratic formula and got:
Z=(-1+ sq rt 7)/2 or Z=(-1- sq rt 7)/2
The answer in the book is:
(z-1)^2 (z+1-i)(z+1+i)
Could anyone tell me where I went wrong?
Thank you for your time in advance.
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
First try check for root of 1 gives . Be sure that your dividend of synthetic division shows ALL degrees of z.

continuing, again if root of 1 is checked, you find factorization . You might have made a visual omission on paper or through keyboard, or maybe forgot about accounting for degrees of z in the division process.

NOW to deal with the quadratic factor,
roots are
.

To conitnue,
, and you simply simplify this obviously complex factorization or keep as linear and quadratic factorization...

-
Either you want it that way, or you want ...
.
RELATED QUESTIONS
Could you please help me out with the following question?? Please... Add z (answered by edjones)

CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Perform the indicated operation. Give... (answered by Fombitz)

Please help me understand how to do this.. Perform the indicated operations and simplify (answered by ewatrrr)

Hi Finding this difficult, new to this can someone please help If z+2+j is one... (answered by Alan3354)

Hi Finding this difficult, new to this can someone please help If z=2+j is one... (answered by Edwin McCravy)

Please help me with this. The question was not given from a book. Solve for X, Y, and Z... (answered by Edwin McCravy)

perform the indicated operations and simplify the following expression 2z-1/z^2+z-6... (answered by KMST)

Please help me solve the question... (answered by Fombitz)

Could you please help me out with this problem???? Simplify z^2-4z-5... (answered by jim_thompson5910)