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Solution - Simplification or other simple results

3x2x+23
3x^2-x+23

Step by Step Solution

Step  1  :

Equation at the end of step  1  :

  (8+((3•(x-2))•x))+5•(x+3)

Step  2  :

Equation at the end of step  2  :

  (8+(3•(x-2)•x))+5•(x+3)

Step  3  :

Equation at the end of step  3  :

  (8 +  3x • (x - 2)) +  5 • (x + 3)

Step  4  :

Trying to factor by splitting the middle term

 4.1     Factoring  3x2-x+23 

The first term is,  3x2  its coefficient is  3 .
The middle term is,  -x  its coefficient is  -1 .
The last term, "the constant", is  +23 

Step-1 : Multiply the coefficient of the first term by the constant   3 • 23 = 69 

Step-2 : Find two factors of  69  whose sum equals the coefficient of the middle term, which is   -1 .

     -69   +   -1   =   -70
     -23   +   -3   =   -26
     -3   +   -23   =   -26
     -1   +   -69   =   -70
     1   +   69   =   70
     3   +   23   =   26
     23   +   3   =   26
     69   +   1   =   70


Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Final result :

  3x2 - x + 23

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