3y - 2
2y =1
2y +2
у
2y - 2

Answer at bottom

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

      (3•(y2))     ((3-(3•(y2)))+y)

 —————————————————+————————————————

 (((2•(y2))+5y)-3)   (2y-1)•(y+3)  

STEP

2

:

Equation at the end of step

2

:

      (3•(y2))      ((3-3y2)+y)

 —————————————————+————————————

 (((2•(y2))+5y)-3) (2y-1)•(y+3)

STEP

3

:

              -3y2 + y + 3  

Simplify   ——————————————————

           (2y - 1) • (y + 3)

Trying to factor by splitting the middle term

3.1     Factoring  -3y2 + y + 3

The first term is,  -3y2  its coefficient is  -3 .

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

The last term, "the constant", is  +3

Step-1 : Multiply the coefficient of the first term by the constant   -3 • 3 = -9

Step-2 : Find two factors of  -9  whose sum equals the coefficient of the middle term, which is   1 .

     -9    +    1    =    -8

     -3    +    3    =    0

     -1    +    9    =    8

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Equation at the end of step

3

:

      (3•(y2))      (-3y2+y+3)

 —————————————————+————————————

 (((2•(y2))+5y)-3) (2y-1)•(y+3)

STEP

4

:

Equation at the end of step

4

:

   (3•(y2))    (-3y2+y+3)

 ————————————+————————————

 ((2y2+5y)-3) (2y-1)•(y+3)

STEP

5

:

Equation at the end of step

5

:

       3y2           (-3y2 + y + 3)  

 —————————————— +  ——————————————————

 (2y2 + 5y - 3)    (2y - 1) • (y + 3)

STEP

6

:

                3y2    

Simplify   ————————————

           2y2 + 5y - 3

Trying to factor by splitting the middle term

6.1     Factoring  2y2 + 5y - 3

The first term is,  2y2  its coefficient is  2 .

The middle term is,  +5y  its coefficient is  5 .

The last term, "the constant", is  -3

Step-1 : Multiply the coefficient of the first term by the constant   2 • -3 = -6

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   5 .

     -6    +    1    =    -5

     -3    +    2    =    -1

     -2    +    3    =    1

     -1    +    6    =    5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -1  and  6

                    2y2 - 1y + 6y - 3

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

                   y • (2y-1)

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

                   3 • (2y-1)

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

                   (y+3)  •  (2y-1)

            Which is the desired factorization

Equation at the end of step

6

:

         3y2             (-3y2 + y + 3)  

 —————————————————— +  ——————————————————

 (2y - 1) • (y + 3)    (2y - 1) • (y + 3)

STEP

7

:

Adding fractions which have a common denominator :

7.1       Adding fractions which have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3y2 + (-3y2+y+3)            y + 3      

————————————————  =  ——————————————————

 (2y-1) • (y+3)      (2y - 1) • (y + 3)

Canceling Out :

7.2    Cancel out  (y + 3)  which appears on both sides of the fraction line.

Final result :

    1  

 ——————

 2y - 1

Step-by-step explanation: