Question

What is the value of h such that 2h-3 \3-5h = - 6 \ 11 ?

Answer 1

Step-by-step explanation: Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

 

STEP

2

:

Equation at the end of step

2

:

 

STEP

3

:

           2h3 - 5h2 + 22h

Simplify   ———————————————

               2h + 3    

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  2h3 - 5h2 + 22h  =   h • (2h2 - 5h + 22)

Trying to factor by splitting the middle term

4.2     Factoring  2h2 - 5h + 22

The first term is,  2h2  its coefficient is  2 .

The middle term is,  -5h  its coefficient is  -5 .

The last term, "the constant", is  +22

Step-1 : Multiply the coefficient of the first term by the constant   2 • 22 = 44

Step-2 : Find two factors of  44  whose sum equals the coefficient of the middle term, which is   -5 .

     -44    +    -1    =    -45

     -22    +    -2    =    -24

     -11    +    -4    =    -15

     -4    +    -11    =    -15

     -2    +    -22    =    -24

     -1    +    -44    =    -45

     1    +    44    =    45

     2    +    22    =    24

     4    +    11    =    15

     11    +    4    =    15

     22    +    2    =    24

     44    +    1    =    45

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Polynomial Long Division :

4.3    Polynomial Long Division

Dividing :  2h2-5h+22

                             ("Dividend")

By         :    2h+3    ("Divisor")

dividend     2h2  -  5h  +  22

- divisor  * h1     2h2  +  3h    

remainder      -  8h  +  22

- divisor  * -4h0      -  8h  -  12

remainder             34

Quotient :  h-4

Remainder :  34

Final result :

 h • (2h2 - 5h + 22)

 ———————————————————

       2h + 3      

See results of polynomial long division:

1. In step #04.03