Question

Which is the factorization of x2 + 8?

(x + 2)(x2 - 2x + 4)
O (x - 2)(x2 + 2x + 4)
O (x + 2)(x2 – 2x + 8)
O (x - 2)(x2 + 2x + 8)

Answer 1

The answer is
`(x+2)(x^2-2x+4)`.

Explanation:

To start, I think you want to know what the factorization of
`x^3+8` is, this because none of the options can give a result with a power lower than 3.

Then, when you choose
`(x+2)(x^2-2x+4)` you have the next:

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

Answer 2

Explanation:

x = 2 • ± √2 = ± 2.8284

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

AB = BA is the commutative property of multiplication.

- AB + AB equals zero and is therefore eliminated from the expression.

8 is not a square !!