Use long division to find the quotient below. (12x3 + 3x2 - 108) = (3x-6)
O A. 4x2 + 6x + 18
O B. 4x2 + 9x + 18
O C. 4x2 - 6x + 18
D. 4x2-9x+18

B

Step-by-step explanation:

12x^3+3x^2-108 = 3x-6

3(4x^3+x^2-36) =3(x-2) ( divide by 3 both sides)

4x^3+x^2-36=x-2

4x^3+x^2-36

4x^3+x^2-36/x-2 =

divisor  4x^2           :(4x^2) (x-2) =4x^3-8x^2

                                 4x^3+x^2-36-4x^-8x^2 =9x^2-36

then divisor is 9x  :      9x(x-2)= 9x^2-18x

the remainder is :          9x^2-18x-9x^2-36 = 18x-36

then divisor is  18:              18(x-2) = 18x-36

subtract : 18x-36-(18x-36)= 0

the answer is 4x^2+9x+18

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.