Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.

2 (multiplicity 2), 3+i (multiplicity 1)

So, I've done this like I learned, but my answer is way different from the one in the back of my book which is x^4-10x^3+38x^2-64x+40

Can somebody explain to me how they got this answer?

Question

Write a polynomial function of minimum degree in standard form with real coefficients whose zeros and their multiplicities include those listed.

2 (multiplicity 2), 3+i (multiplicity 1)

So, I've done this like I learned, but my answer is way different from the one in the back of my book which is x^4-10x^3+38x^2-64x+40

Can somebody explain to me how they got this answer?

anonymous · Answer

Hmm, seems there is some missing information that you had to assume yourself.

anonymous · Answer

It says "with real coefficients" which means that complex roots must come in conjugate pairs. If 3+i is a root then so is 3-i.

anonymous · Answer

Ohh, I didn't know that. That helps a lot.. So, in setup, it should look like this, 
(x-2)^2*(x-(3-i))(x-(3+i))?

anonymous · Answer

Yes, that looks right.

anonymous · Answer

But then, how do i multiply (x-3-i)(x+3+i)?

anonymous · Answer

It's like FOILing (distributive property), but there are three terms to distribute to three terms.