Iam so confused and im really struggling and this is the only question i need

A polynomial of degree 3 has exactly 3 solutions if we use complex numbers. If the polynomial has real coefficients and z is a complex solution, i.e., , the conjugate is also a solution:

So, in the first case, if we know that 1-i is a solution, the conjugate 1+i must be a solution as well.

So, we know all the roots: -5, 1+i, 1-i.

When you know the solutions of a polynomial, you can write the polynomial (up to multiples) as

So, in your case, we have

You can check that indeed , because the constant term is 10, so, we're ok with this

The second exercise is exactly the same: the solutions -6, i, -i identify the polynomial

In this case, P(-3)=30, so if we want P(-3)=60 we have to multiply everything by 2:

the fist one is not equalvalent but i think th second one isand the third isnt definetly or the last one is i think. hope this !

step-by-step explanation: