Answer:
(3x2−2)⋅(2x−3)
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(((6 • (x3)) - 32x2) - 4x) + 6
STEP
2
:
Equation at the end of step
2
:
(((2•3x3) - 32x2) - 4x) + 6
STEP
3
:
Checking for a perfect cube
3.1 6x3-9x2-4x+6 is not a perfect cube
Trying to factor by pulling out :
3.2 Factoring: 6x3-9x2-4x+6
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -4x+6
Group 2: 6x3-9x2
Pull out from each group separately :
Group 1: (2x-3) • (-2)
Group 2: (2x-3) • (3x2)
-------------------
Add up the two groups :
(2x-3) • (3x2-2)
Which is the desired factorization
Trying to factor as a Difference of Squares:
3.3 Factoring: 3x2-2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 3 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
(3x2 - 2) • (2x - 3)
