How To Factor X^3-8 – Solve Simplification Or Other Simple Results X3

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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