Question

The polynomial x3 + 8 is equal to (x + 2)(x2 – 2x + 4). (x – 2)(x2 + 2x + 4). (x + 2)(x2 – 2x + 8). (x – 2)(x2 + 2x + 8).

Answer 1

The polynomial x^3 + 8 can be factored as (x + 2)(x^2 - 2x + 4) by applying the sum of cubes factorization formula a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Step-by-step explanation:

The question is focused on verifying the equality between a given polynomial and a set of factorized expressions. Specifically, we want to determine which of the options provided correctly factors the polynomial x^3 + 8.

Let's recall that the sum of cubes can be factored as a^3 + b^3 = (a + b)(a^2 - ab + b^2). In our case, we can see x^3 + 8 as x^3 + 2^3, which means that 8 is a perfect cube (2^3).

Using the sum of cubes formula, the given polynomial can be factored as follows:
x^3 + 8 = x^3 + 2^3 = (x + 2)(x^2 - 2x + 4).

Answer 2

(x + 2)(x² – 2x + 4)

Step-by-step explanation:

To determine if this expression is equal to x³+8, use the distributive property:

x(x²)+x(-2x)+x(4)+2(x²)+2(-2x)+2(4)

x³-2x²+4x+2x²-4x+8

Rearranging this to group like terms together,

x³-2x²+2x²+4x-4x+8

Combining like terms, we see that

-2x²+2x² = 0

and

4x-4x = 0. This leaves us with

x³+8