Use the remainder theorem to determine whether x - 2 is a factor of
f(x) = x3 + 3x2 - x - 18

a)
yes, x - 2 is a factor of f(x) because f(2) = 0

b)
no, x - 2 is not a factor of f(x) because f(2) = 0

c)
yes, x - 2 is a factor of f(x) because f(-2) = -12

d)
no, x - 2 is not a factor of f(x) because f(-2) = -12

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: