Question

Factor the polynomial

X^3 + 8

Answer 1

google "sum of cubes"

x^3 + 2^3

Answer 2

To factor x³ + 8 you must use sum of cubes formula:

A³ + B³ = ( A + B ) ( A² - A ∙ B + B² )

In this case :

A = x

B = 2

becouse 2³ = 8

So:

x³ + 8 = x³ + 2³

x³ + 2³ = ( x + 2 ) ( x² - x ∙ 2 + 2² ) =

( x + 2 ) ( x² - 2 x + 4 )

x² - 2 x + 4 can't be factoring becouse discriminant of x² - 2 x + 4:

D = b² - 4 ∙ c = ( - 2 )² - 4 ∙ 1 ∙ 4 = 4 - 16 = - 12

This mean:

x² - 2 x + 4 has two complex solutions and can't be factoring with real numbers.

Solution:

x³ + 8 = ( x + 2 ) ( x² - 2 x + 4 )

Answer 3

[AI-generated answer — Explain Bot]

To factor the polynomial x^3 + 8, we can use the formula for factoring the sum of two cubes.

The formula for factoring a sum of two cubes is:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In our case, a = x and b = 2, since 2^3 = 8.

Using the formula, we have:

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

Therefore, the factored form of the polynomial x^3 + 8 is (x + 2)(x^2 - 2x + 4).