Question

Simplify fully: X^2+3x-4/ 2x^2-5x+3

Answer 1

Answer:

(-x - 3) • (x - 1)

Step-by-step explanation:

Step  1  :

           2

Simplify   —

           1

Equation at the end of step  1  :

 ((((x2)+3x)-(2•x2))-5x)+3

Step  2  :

Equation at the end of step  2  :

 ((((x2) +  3x) -  2x2) -  5x) +  3

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  -x2 - 2x + 3  =   -1 • (x2 + 2x - 3)

Trying to factor by splitting the middle term

4.2     Factoring  x2 + 2x - 3

The first term is,  x2  its coefficient is  1 .

The middle term is,  +2x  its coefficient is  2 .

The last term, "the constant", is  -3

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

Step-2 : Find two factors of  -3  whose sum equals the coefficient of the middle term, which is   2 .

     -3    +    1    =    -2

     -1    +    3    =    2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  3

                    x2 - 1x + 3x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-1)

Step-5 : Add up the four terms of step 4 :

                   (x+3)  •  (x-1)

            Which is the desired factorization

Final result :

 (-x - 3) • (x - 1)

Processing ends successfully

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Answer 2

Answer:

-x2 - 8x - 3

Step-by-step explanation:

((((x2)-3x)-(2•x2))-5x)-3

((((x2) -  3x) -  2x2) -  5x) -  3

Pull out like factors :

-x2 - 8x - 3  =   -1 • (x2 + 8x + 3)

Factoring  x2 + 8x + 3