Question

The polynomial x^3+8 is equal to

Answer 1

(x + 2)(x² - 2x + 4)

Explanation:

x³ + 8 ← is a sum of cubes, which factors in general as

• a³ + b³ = (a + b)(a² - ab + b²)

x³ = (x)³ ⇒ a = x and 8 = 2³ ⇒ b = 2

x³ + 8 = (x + 2)(x² - 2x + 4) ← in factored form

Answer 2

`x^(3) +8=(x+2)(x^(2) -2x+4)`

Explanation:

The binomial can be factored by the binomial form by trinomial. This binomial is a sum of cubes, whose general form presents the following result.

`(x^(3) +y^(3) )=(x+y)(x^(2) -xy+y^(2) )`

Substituting the values ​​of x and y we will have

`x^(3) =x^(3) ;     y^(3) =8`

Obtaining the cubic roots of each variable

`x=x; y=2`

So

`x^(3) +8=(x+2)(x^(2) -2x+4)`