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.                            

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.