Divide the polynomials. x^3+6x^2-5x by x-2

Step-by-step explanation:

Easiest way is to use synthetic division, but I am going to use comparing coefficients because I have my phone:

x³ + 6x² - 5x

= (x - 2)(Ax² + Bx + C) + D

= Ax³ + (B - 2A)x² + (C - 2B)x + (D - 2C)

By Comparing Coefficients, we have

A = 1

B - 2A = 6

C - 2B = -5

D - 2C = 0

Solving, we have A = 1, B = 8, C = 11, D = 22.

Hence x³ + 6x² - 5x

= (x - 2)(x² + 8x + 11) + 22.

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

  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).