Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? select two options

The missing term is 4x

The missing term is 16x

Step-by-step explanation:

* Lets explain how to solve the problem

- The polynomial is 36x³ - 22x² - ..............

- We need to find the missing term such that the greatest common

 factor of the resulting polynomial is 2x

∵ The greatest power of x is 3, and there is another term with x²,

   then the missing term must have x to have a greatest common

   factor of the variable = x

∵ The coefficients of the given terms are 36 and 22 , the greatest

  common factor of them is 2 so we must to chose the coefficient

  of the missing term with a factor 2

# Option 1:

∵ the missing term is 4x

∵

∵

∵

∴ 36x³ - 22x² - 4x = 2x(18x² - 11x - 2)

* The missing term is 4x

# Option 2:

∵ the missing term is 16x

∵

∵

∵

∴ 36x³ - 22x² - 16x = 2x(18x² - 11x - 8)

* The missing term is 16x

  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).