1. ## factorosation of polynomials

Hi the question says If z-3i is a factor of 2z^4-4z^3+21z^2-36z+27, find the remaining factors.

I tried doing long division by dividing it by 2z+9 but i get a crazy fraction answer with a remainder which looked wrong, is their another way i can approach this.? and im working in the chapter factorasation of polynomials of C. someone suggested synthetic division but when i used that with 3i, i got zero as a answer

The answer in the book is z+3i, z-1 (plus+, minus-) 1 (over) root2i

Please can you guys try to answer this i spend like half a day trying to figure this out.

thanks

2. Why would you divide by $\displaystyle \displaystyle 2z + 9$? You're supposed to divide by $\displaystyle \displaystyle z^2 + 9$...

3. Originally Posted by iFuuZe
Hi the question says If z-3i is a factor of 2z^4-4z^3+21z^2-36z+27, find the remaining factors.

I tried doing long division by dividing it by 2z+9 but i get a crazy fraction answer with a remainder which looked wrong, is their another way i can approach this.? and im working in the chapter factorasation of polynomials of C. someone suggested synthetic division but when i used that with 3i, i got zero as a answer

The answer in the book is z+3i, z-1 (plus+, minus-) 1 (over) root2i

Please can you guys try to answer this i spend like half a day trying to figure this out.

thanks
All the coefficients are real and so the conjugate root theorem can be used. Therefore z + 3i is a factor. Therefore (z + 3i)(z - 3i) = z^2 + 9 is a factor. Divide z^2 + 9 into the polynomial to get the quadratic factor and then factorise it.