# factoring with complex numbers

• Sep 13th 2009, 03:24 AM
solarscott
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:

x=i

therefore after simplifying:
P(i)=(1+q)+i(2-p)

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?

Thanks

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
• Sep 13th 2009, 03:59 AM
Quote:

Originally Posted by solarscott
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:
x=i

therefore after simplifying:
P(i)=(1+q)+i(2-p)

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?

Thanks

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

Hi

$(x^2+1)(ax^2+bx+c)=x^4+px^3+2x+q$

$ax^4+bx^3+(c+a)x+bx+c$

By comparing ,

b=2 , p=2 , q=-1 , c=-1 , a=1

So now

$
x^4+2x^3+2x-1=(x^2+1)(x^2+2x-1)
$
• Sep 13th 2009, 04:23 AM
solarscott
Thanks, that's the same answer I ended up coming up with...just in a different way.

In the question it asks to factorize over C...this has been done because there is no complex component?

by the way...how do you get your equations into images?

Thanks again
• Sep 13th 2009, 08:12 AM
Quote:

Originally Posted by solarscott
Thanks, that's the same answer I ended up coming up with...just in a different way.

In the question it asks to factorize over C...this has been done because there is no complex component?

by the way...how do you get your equations into images?

Thanks again

X^2+1 is complex and the other one is real .. you can check by finding its discriminant . I think that's what the question meant .

Put equation into images , i am not really sure .. but you can pm the moderators and ask them .