Question

Solve the equation by factoring
81m^3-81m^2-36m+36=0
​

Answer 1

The solution set is {1, -2/3, 2/3}.

Explanation:

81m^3-81m^2-36m+36=0

9(9m^3 - 9m^2 - 4m + 4) = 0

Looks like 1 might be one root:

f(1) = = 9*1 - 9*1 - 4*1 + 4 = 0 so one factor is (x - 1).

Divide the function by x - 1:

9m^2 - 4 <------------------Quotient

----------------------------------

m - 1 ) 9m^3 - 9m^2 - 4m + 4

9m^3-9m^2

-----------------------

-4m + 4

-4m + 2

..............

Now :

9m^2 - 4 = (3m - 2)(3m + 2).

so m - 1 = 0 or 3m - 2 = 0 or 3m + 2 = 0

m = 1 , 2/3, -2/3.