Answer:

Step-by-step explanation:
We want to find the minimum-degree polynomial with real coefficients and zeros at:

As well as a <em>y-</em>intercept of 64.
By the Complex Root Theorem, if <em>a</em> + <em>b</em>i is a root, then <em>a</em> - <em>b</em>i is also a root.
So, a third root will be 4 - 4i.
The factored form of a polynomial is given by:

Where <em>a</em> is the leading coefficient and <em>p</em> and <em>q</em> are the zeros. More factors can be added if necessary.
Substitute:

Since we want the minimum degree, we won't need to add any exponents.
Expand the second and third factors:

Hence:

Lastly, we need to determine <em>a</em>. Since the <em>y-</em>intercept is <em>y</em> = 64, this means that when <em>x</em> = 0, <em>y</em> = 64. Thus:

Solve for <em>a: </em>

Our factored polynomial is:

Finally, expand:
