SOLUTION: need help fatoring this polynomial completely. 8x^3 + 4x^2 - 2x-1 and use the square root property to solve the equation. (1-x)^2 = 4.

8x³+4x²-2x-1

Factor 4x² out of the first two terms:

4x²(2x+1)-2x-1

Factor -1 out of the last two terms:

4x²(2x+1)-1(2x+1)

Now there are just two terms. Factor (2x+1) out of those 
two terms:

(2x+1)(4x²-1)

Factor the second factor as the difference of two squares:

(2x+1)(2x-1)(2x+1)

and since the (2x-1) appears twice as a factor:

(2z+1)²(2x-1)

Edwin

Here is your second problem:

(1-x)² = 4

Use the principle of square roots which says this: 

The equation 
             " A² = B " 

is equivalent to the double equation (actually two equation)
 
              " A = ±√B "

              where ± means use + one time and use - a second time
              to make two equations:   

1-x = ±√4 

1-x = ±2

Using the +              Using the -

1-x = 2                  1-x = -2
 -x = 1                   -x = -3
  x = -1                   x = 3

There are two solutions:  -1 and 3     

Edwin