Is x-2 a factor of 4x^5 +5x^4 +1?

No

Step-by-step explanation:

By the Factor theorem

If (x - h) is a factor of f(x) then f(h) = 0

Here (x - 2) with h = 2 and f(x) = 4 + 5 + 1 , then

f(2) = 4 + 5 + 1

     = 4(32) + 5(16) + 1

     = 128 + 80 + 1

     = 209

Since f(2) ≠ 0 then ( x - 2) is not a factor

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.