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# long division

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(x^3+250x^2+100x) / (1\2x^2+25x+9)

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#1
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(x(3)+250x(2)+100x)/((1)/(2)x(2)+25x+9)

Final result :

2x • (x2 + 250x + 100) —————————————————————— x2 + 50x + 18

Step by step solution :

Step  1  :

1 Simplify — 2

Equation at the end of step  1  :

x)1 ————•x2)+25x)+9) (((2

Step  2  :

Equation at the end of step  2  :

)x2 ———+25x)+9) ((2

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

25x 25x • 2 25x = ——— = ——————— 1 2

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 :

3.2       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:

x2 + 25x • 2 x2 + 50x ———————————— = ———————— 2 2

Equation at the end of step  3  :

(x2+50x) ————————+9) (2

Step  4  :

Rewriting the whole as an Equivalent Fraction :

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  2  as the denominator :

9 9 • 2 9 = — = ————— 1 2

Step  5  :

Pulling out like terms :

5.1     Pull out like factors :

x2 + 50x  =   x • (x + 50)

Adding fractions that have a common denominator :

5.2       Adding up the two equivalent fractions

x • (x+50) + 9 • 2 x2 + 50x + 18 —————————————————— = ————————————— 2 2

Equation at the end of step  5  :

(x2+50x+18) ——————————— 2

Step  6  :

Equation at the end of step  6  :

(x2 + 50x + 18) ——————————————— 2

Step  7  :

x2+50x+18 Divide x3+250x2+100x by ————————— 2

Step  8  :

Pulling out like terms :

8.1     Pull out like factors :

x3 + 250x2 + 100x  =   x • (x2 + 250x + 100)

Trying to factor by splitting the middle term

8.2     Factoring  x2 + 250x + 100

The first term is,  x2  its coefficient is  1 .
The middle term is,  +250x  its coefficient is  250 .
The last term, "the constant", is  +100

Step-1 : Multiply the coefficient of the first term by the constant   1 • 100 = 100

Step-2 : Find two factors of  100  whose sum equals the coefficient of the middle term, which is   250 .

-100   +   -1   =   -101

-50   +   -2   =   -52

-25   +   -4   =   -29

-20   +   -5   =   -25

-10   +   -10   =   -20

-5   +   -20   =   -25

For tidiness, printing of 12 lines which failed to find two such factors, was suppressed

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

Trying to factor by splitting the middle term

8.3     Factoring  x2+50x+18

The first term is,  x2  its coefficient is  1 .
The middle term is,  +50x  its coefficient is  50 .
The last term, "the constant", is  +18

Step-1 : Multiply the coefficient of the first term by the constant   1 • 18 = 18

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   50 .

-18   +   -1   =   -19

-9   +   -2   =   -11

-6   +   -3   =   -9

-3   +   -6   =   -9

-2   +   -9   =   -11

-1   +   -18   =   -19

1   +   18   =   19

2   +   9   =   11

3   +   6   =   9

6   +   3   =   9

9   +   2   =   11

18   +   1   =   19

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

Final result :

2x • (x2 + 250x + 100) —————————————————————— x2 + 50x + 18

Splatmaster  Nov 29, 2017
#3
+91956
0

I have no idea what you are on about Splatmaster.

Melody  Nov 29, 2017
#2
+91956
0

(x^3+250x^2+100x) / (1\2x^2+25x+9)

The meaning of the question is not clear.

What is the backwards slash for?

If it is a divide sign is the 1 divided by everything after it or is it only divided by the 2 or perhaps by only the 2x^2   ??

Melody  Nov 29, 2017
#4
+84237
+1

(x^3+250x^2+100x) / (1\2x^2+25x+9)  =

(2x^3 + 500x^2   + 200x)  / ( x^2 + 50x  + 18 )

2x  +  400

x^2 + 50x   +  18  [   2x^3   +  500x^2    +  200x  ]

2x^3   + 100x^2    +    36x

_______________________

400x^2  + 164x

400x^2 +   20000x  + 7200

____________________

-19836x -  7200

CPhill  Nov 29, 2017

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