(3x^3 + 4x²) - (2x^3 + 3x^2 -x)

 x • (x^2 + x + 1)

Step-by-step explanation:

Step  1  :

Equation at the end of step  1  :

 ((3•(x^3))+(4•(x^2)))-(((2•(x^3))+3x^2)-x)

Step  2  :

Equation at the end of step  2  :

 ((3•(x^3))+(4•(x^2)))-((2x^3+3x^2)-x)

Step  3  :

Equation at the end of step  3  :

 ((3 • (x^3)) +  22x^2) -  (2x^3 + 3x^2 - x)

Step  4  :

Equation at the end of step  4  :

 (3x^3 +  22x^2) -  (2x^3 + 3x^2 - x)

Step  5  :

Step  6  :

Pulling out like terms :

6.1     Pull out like factors :

  x^3 + x^2 + x  =   x • (x^2 + x + 1)

Trying to factor by splitting the middle term

6.2     Factoring  x^2 + x + 1

The first term is,  x^2  its coefficient is  1 .

The middle term is,  +x  its coefficient is  1 .

The last term, "the constant", is  +1

Step-1 : Multiply the coefficient of the first term by the constant  1 • 1 = 1

Step-2 : Find two factors of  1  whose sum equals the coefficient of the middle term, which is   1 .

     -1    +    -1    =    -2

     1    +    1    =    2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 x • (x^2 + x + 1)

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