Question

Which is the factorization of x3 + 8?

Answer 1

Answer:

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

Step-by-step explanation:

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Answer 2

Answer:

The factorization of $x^{3}+8$ is $(x+2)(x^{2} -2x+4)$

Step-by-step 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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