SOLUTION: using long divison perform the following (1+x^2+6x^2) divided by (2x-1)

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Question 805475: using long divison perform the following (1+x^2+6x^2) divided by (2x-1)
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Did you make a mistake? (1+x+6x^2) or (1+x^2+6x^2)?

If meant as you wrote, then you have 1%2B7x%5E2 to divide by 2x-1. Your dividend must show all degrees of x, so you want %287x%5E2%2B0%2Ax%2B1%29%2F%282x-1%29.


________|_____(7/2)x_________(7/4)
_____________________________________________
________|
2x-1____|_____7x%5E2__________0%2Ax___________1
________|_____7x%5E2__________-%287%2F2%29x
____________________________________
_______________0___________%287%2F2%29x________1
___________________________%287%2F2%29x________-%287%2F4%29
_______________________________________________
______________________________0_________1%2B%287%2F4%29


Start by asking what is %287x%5E2%29%2F%282x%29?
The result is %287%2F2%29x, which you put into the quotient line, directly above 7x%5E2.
'
Multiply 2x-1 by (7/2)x and subtract this result from the first TWO TERMS of the dividend.
'
Bring down the next term, the "1"...
...
Other steps are similar...

The remainder should be simplified 4%2F4%2B7%2F4=11%2F4
And its meaning is %2811%2F4%29%2F%282x-1%29=11%2F%284%282x-1%29%29=highlight%2811%2F%288x-4%29%29