All such non-zero polynomials difference by a constant multiple. So we will find one which has 1 as its leading coefficient (called monic).

Now if f(x) is a polynomial in R[x] (meaning the real numbers) and if a+bi is a zero then a-bi is also a zero.

So if 3+i is a zero that means 3-i is a zero.

Thus,

Multiply the last two factors together,