Find the polynomial of minimum degree, with real coefficients, zeros at x=4±2⋅i and x=−8, and y-intercept at −480. Write your answer in standard form.

The polynomial of minimum degree is .

Step-by-step explanation:

According to the statement, we appreciate that polynomial pass through the following points:

(i) , (ii) , (iii) , (iv)

From Algebra we know that any n-th grade polynomial can be constructed by knowing n+1 different points. Hence, the polynomial of minimum degree is a quartic function. The polynomial has the following form:

We proceed to expand the expression until standard form is obtained:

If we know that , then:

Then, the polynomial is:

The polynomial of minimum degree is .

linear pair postulates