Factoring Polynomials Help..

If P(x)=3x^{3}+x^{2}+48x+16 contains the factor x-4i, find all the remaining factors. Write p(x) in factored form.

So I have (x-4i) and (x+4i) as two factors which = (x^{2}+16)

I then divide using long polynomial division. (3x^{2}+x+48x+16)/(x+16) = 3x+1 with no remainders.

I find that (x-4i),(x+4i) and (3x+1) are all factors of the polynomial P(x).....Are these all the factors? Did I do this correctly?

Thank you very much

Re: Factoring Polynomials Help..

Quote:

Originally Posted by

**curt26** If P(x)=3x^{3}+x^{2}+48x+16 contains the factor x-4i, find all the remaining factors. Write p(x) in factored form.

$\displaystyle \\3x^3+x^2+48x+16\\x^2(3x+1)+16(3x+1)\\(x^2+16)(3x +1)$

Re: Factoring Polynomials Help..

Thank you,

So you're saying the only factors are (x^{2}+16) and (3x+1)?

Re: Factoring Polynomials Help..

Quote:

Originally Posted by

**curt26** So you're saying the only factors are (x^{2}+16) and (3x+1)?

Well not exactly. From that you see the roots are $\displaystyle \pm4i~\&~\tfrac{-1}{3}$.

Re: Factoring Polynomials Help..

Ok, so if my roots are +4i, -4i and -1/3 the factors should be (x-4i),(x+4i) and (3x+1)? Unless I'm confused somewhere..

Thank you