### Reformatting the input :

Changes made to your input should not affect the solution: (1): “x3” was replaced by “x^3”.

You are watching: How to factor x^3-8

## Step 1 :

Trying to factor as a Difference of Cubes:1.1 Factoring: x3-8 Theory : A difference of two perfect cubes, a3-b3 can be factored into(a-b)•(a2+ab+b2)Proof:(a-b)•(a2+ab+b2)=a3+a2b+ab2-ba2-b2a-b3 =a3+(a2b-ba2)+(ab2-b2a)-b3=a3+0+0-b3=a3-b3Check:8is the cube of 2Check: x3 is the cube of x1Factorization is :(x – 2)•(x2 + 2x + 4)

Trying to factor by splitting the middle term

1.2Factoring x2 + 2x + 4 The first term is, x2 its coefficient is 1.The middle term is, +2x its coefficient is 2.The last term, “the constant”, is +4Step-1 : Multiply the coefficient of the first term by the constant 1•4=4Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 2.

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-4 | + | -1 | = | -5 | ||

-2 | + | -2 | = | -4 | ||

-1 | + | -4 | = | -5 | ||

1 | + | 4 | = | 5 | ||

2 | + | 2 | = | 4 | ||

4 | + | 1 | = | 5 |

Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored

## Final result :

(x – 2) • (x2 + 2x + 4)

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