Complex Long Division Please Help (1 Viewer)

[Jack Trumper]

We kinda rushed through this at the end of term and i wasn't payingm uch attention D ) and i dont follow the example (i think i only half finished it ).

Can someone please write out the solution step-by-step to this given question, after someone does this question I should be able to understand the method (I learn by examples).

Question: Find the remainder when P(x) = x^3 + 2x^2 + 1 is divided by (a) x + i (b) x^2 + 1


Thanks a heap.

 

[KeypadSDM]

Oh god. I'll have to do this tomorrow. I HATED Division.

 

[turtle_2468]

you mean, I have to do it

a) you can do this part by the remainder theorem (see 3 unit). So the remainder is equal to P(-i) (as the factor divided by is (x-(-i)) ) which is (-i)^3+2(-i)^2+1=i-2+1
which is i-1.

b) This is harder. Treat it as normal division by polynomial...
Hence the first term of the quotient would be x (so (x^3+2x^2+1)-(x(x^2+1)) leaves (2x^2-x+1) ). The second term of the quotient would be 2 as you want to get rid of the highest power of x ie 2x^2.
So (2x^2-x+1)-(2(x^2+1)) leaves (-x-3) as the final remainder.

PS Sorry for not being there all the time these holidays, I've been in Melbourne and going to katoomba next week... and by the time I check (usually daily) someone has normally answered the q anyway

 

[ND]

Originally posted by turtle_2468

leaves (-x-3) as the final remainder.

(-x-1).

 

[turtle_2468]

umm. yes.