Simplify the given expression 8x^2-8/ x / 8(x^2 + 8)/26x^2 - 31x

-x • (x2 - 208x + 814)

 ——————————————————————

           26          

Step-by-step explanation:

Step  1  :

           x2 + 8

Simplify   ——————

             26  

Polynomial Roots Calculator :

  Find roots (zeroes) of :       F(x) = x2 + 8

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  8.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,4 ,8

Let us test

 P    Q    P/Q    F(P/Q)    Divisor

     -1       1        -1.00        9.00      

     -2       1        -2.00        12.00      

     -4       1        -4.00        24.00      

     -8       1        -8.00        72.00      

     1       1        1.00        9.00      

     2       1        2.00        12.00      

     4       1        4.00        24.00      

     8       1        8.00        72.00      

Polynomial Roots Calculator found no rational roots

Equation at the end of step  1  :

             8     (x2+8)

 ((8•(x2))-((— ÷ 8•——————)•x2))-31x

             x       26  

:

           8

Simplify   —

           x

Equation at the end of step  2  :

             8     (x2+8)

 ((8•(x2))-((— ÷ 8•——————)•x2))-31x

             x       26  

        8      

Divide  —  by  8

        x      

             1 (x2+8)

 ((8•(x2))-((—•——————)•x2))-31x

             x   26  

Equation at the end of step  4  :

                 (x2 + 8)            

 ((8 • (x2)) -  (———————— • x2)) -  31x

                   26x                

Dividing exponential expressions :

 x2 divided by x1 = x(2 - 1) = x1 = x

Equation at the end of step  5  :

                x • (x2 + 8)      

 ((8 • (x2)) -  ————————————) -  31x

                     26          

Equation at the end of step  6  :

          x • (x2 + 8)      

 (23x2 -  ————————————) -  31x

               26          

Rewriting the whole as an Equivalent Fraction :

  Subtracting a fraction from a whole

Rewrite the whole as a fraction using  26  as the denominator :

            23x2     23x2 • 26

    23x2 =  ————  =  —————————

             1          26    

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

    Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

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

23x2 • 26 - (x • (x2+8))      -x3 + 208x2 - 8x

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

           26                       26        

Equation at the end of step  7  :

 (-x3 + 208x2 - 8x)    

 —————————————————— -  31x

         26            

Rewriting the whole as an Equivalent Fraction :

Subtracting a whole from a fraction

Rewrite the whole as a fraction using  26  as the denominator :

          31x     31x • 26

   31x =  ———  =  ————————

           1         26    

Pulling out like terms :

   Pull out like factors :

  -x3 + 208x2 - 8x  =   -x • (x2 - 208x + 8)  

Trying to factor by splitting the middle term

     Factoring  x2 - 208x + 8  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -208x  its coefficient is  -208 .

The last term, "the constant", is  +8  

Multiply the coefficient of the first term by the constant   1 • 8 = 8  

Find two factors of  8  whose sum equals the coefficient of the middle term, which is   -208 .

     -8    +    -1    =    -9  

     -4    +    -2    =    -6  

     -2    +    -4    =    -6  

     -1    +    -8    =    -9  

     1    +    8    =    9  

     2    +    4    =    6  

     4    +    2    =    6  

     8    +    1    =    9  

Adding fractions that have a common denominator :       Adding up the two equivalent fractions

-x • (x2-208x+8) - (31x • 26)     -x3 + 208x2 - 814x

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

             26                           26        

Pulling out like terms :

10.1     Pull out like factors :

  -x3 + 208x2 - 814x  =   -x • (x2 - 208x + 814)  

Trying to factor by splitting the middle term

10.2     Factoring  x2 - 208x + 814  

The first term is,  x2  its coefficient is  1 .

The middle term is,  -208x  its coefficient is  -208 .

The last term, "the constant", is  +814  

Multiply the coefficient of the first term by the constant   1 • 814 = 814  

Find two factors of  814  whose sum equals the coefficient of the middle term, which is   -208 .

     -814    +    -1    =    -815  

     -407    +    -2    =    -409  

     -74    +    -11    =    -85  

     -37    +    -22    =    -59  

     -22    +    -37    =    -59  

     -11    +    -74    =    -85  

     -2    +    -407    =    -409  

     -1    +    -814    =    -815  

     1    +    814    =    815  

     2    +    407    =    409  

     11    +    74    =    85  

     22    +    37    =    59  

     37    +    22    =    59  

     74    +    11    =    85  

     407    +    2    =    409  

     814    +    1    =    815  

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.