1. ## Factoring Polynomials Help..

If P(x)=3x3+x2+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 = (x2+16)

I then divide using long polynomial division. (3x2+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

2. ## Re: Factoring Polynomials Help..

Originally Posted by curt26
If P(x)=3x3+x2+48x+16 contains the factor x-4i, find all the remaining factors. Write p(x) in factored form.
$\displaystyle \\3x^3+x^2+48x+16\\x^2(3x+1)+16(3x+1)\\(x^2+16)(3x +1)$

3. ## Re: Factoring Polynomials Help..

Thank you,

So you're saying the only factors are (x2​+16) and (3x+1)?

4. ## Re: Factoring Polynomials Help..

Originally Posted by curt26
So you're saying the only factors are (x2​+16) and (3x+1)?

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

5. ## 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