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6x^3 - 9x^2 + 4x - 6​

1 Answer

5 votes

Answer:

(3x2−2)⋅(2x−3)

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)

User Rop
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