30+ points need it asap! :) pls show work. Write a polynomial function f of least degree with the following zeros: 3, 4 + i

Or:

Step-by-step explanation:

To find our factors, we can work backwards.

We know that 3 is a zero. This means that:

Subtract 3 from both sides:

So, (x-3) is one of our factors.

We also know that (4+i) is a zero. So:

First, let’s isolate the imaginary. So, subtract 4 from both sides:

Now, let’s square both sides:

Expand the left. Evaluate the right:

Add 1 to both sides. So, our factor is:

Hence, our polynomial function is:

This is also the least degree since we did the most minimum we can do to solve backwards.

Further Notes:

If we want to convert this to standard form, we can distribute:

Combining like terms will yield: