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.

 -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)

abc
a
x
y
/
|abs|
( )
7
8
9
*
4
5
6

%
1
2
3
+
0
,
.

=
abc
a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
p
q
r
s
t
u
v
w
x
y
z

.