Reformatting the intake :
Changes made to her input should not affect the solution: (1): "x3" was changed by "x^3".You are watching: Which is the factorization of x3 + 8?
Step 1 :
Trying to variable as a difference of Cubes:1.1 Factoring: x38 theory : A difference of two perfect cubes, a3b3 have the right to be factored into(ab)•(a2+ab+b2)Proof:(ab)•(a2+ab+b2)=a3+a2b+ab2ba2b2ab3 =a3+(a2bba2)+(ab2b2a)b3=a3+0+0b3=a3b3Check:8is the cube that 2Check: x3 is the cube the x1Factorization is :(x  2)•(x2 + 2x + 4)
Trying to aspect by dividing the middle term1.2Factoring x2 + 2x + 4 The first term is, x2 its coefficient is 1.The middle term is, +2x that is coefficient is 2.The last term, "the constant", is +4Step1 : main point the coefficient of the very first term by the constant 1•4=4Step2 : uncover two components of 4 whose sum equals the coefficient of the center term, i beg your pardon is 2.
4  +  1  =  5  
2  +  2  =  4  
1  +  4  =  5  
1  +  4  =  5  
2  +  2  =  4  
4  +  1  =  5 
Observation : No two such components can be uncovered !! Conclusion : Trinomial can not it is in factored
Final result :
(x  2) • (x2 + 2x + 4)Why learn this
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