Question

Which is the factorization of x3 + 8?

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

PLEASE HELP

Answer 1

a: (x+2)(x^2-2x+4)

Explanation:

i just did on edgen 2020

Answer 2

The factorization of
`x^(3)+8` is
`(x+2)(x^(2) -2x+4)`

Explanation:

The problem is a sum of cubes factorization, this type of factorization applies only in binomials of the form
`(a^(3) +b^(3) )` which means numbers that have exact cubic root and the exponents of the letters a and b are multiples of three.

Sum of cubes equation

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

So, let's factor
`x^(3)+8`

we have to bring the equation to the form
`(a^(3) +b^(3) )`

`x^(3)+8=x^(3)+2^(3)` con
`a=x` y
`b=2`

Solving using sum of cubes equation

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

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

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