(picture) multiplying polynomials and simplifying expressions

(x + 2)(x² - 2x +4)

Step-by-step explanation:

The sum of cubes factors as ...

  (a³ +b³) = (a +b)(a² -ab +b²)

Here, you have a=x, b=2, so the factorization is ...

  x³ +8 = (x +2)(x² -2x +4) . . . . . . matches the first selection

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

if x = 1, then the answer is 3.5