1. write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form.
4, -8, and 2 + 5i

f(x) = x4 - 6x3 - 20x2 + 122x - 928

f(x) = x4 - 19x2 + 244x - 928

f(x) = x4 - 6x3 + 20x2 - 122x + 928

f(x) = x4 - 61x2 + 244x - 928

Option 2 -          

Step-by-step explanation:

Given : Zeros of the polynomial 4, -8, and 2 + 5i.

To find : Write a polynomial function of minimum degree with real coefficients whose zeros include those listed ?

Solution :

The zeros of the polynomial are 4, -8, and 2 + 5i.

There is one conjugate exist i.e. 2-5i.

So, The polynomial form of zeros are      

Multiply the factors i.e. first two terms and other two terms multiply each other,

Therefore, Option 2 is correct.                            

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

add 5 subtract 1

step-by-step explanation: