factoring with complex numbers
Another question...well more of a clarification of a question. Here is the question:
Find the values of the real numbers p and q if x^2+1 is a factor of the polynomial P(x)=x^4+px^3+2x+q. Hence, factorise over R and over C.
I've determined that:
therefore after simplifying:
But now a little bit unsure of what to do. Does this mean that q=-1, and p=2
Then how do I factorize over R and C?
mmm, think I just figured it out...Im gonna use synthetic division to find the remaining roots (assuming it works out nicely) but still not sure what the deal is with C