Step 1 :

Equation at the end of step 1 : 23x3 - 64

Step 2 :

Step 3 :

Pulling out like terms :3.1 Pull out lượt thích factors:8x3 - 64=8•(x3 - 8)

Trying to lớn factor as a Difference of Cubes:3.2 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 khổng lồ factor by splitting the middle term

3.3Factoring 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.

-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 :

8 • (x - 2) • (x2 + 2x + 4)




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