SOLUTION: use long division to find the quotient when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1

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Question 382921: use long division to find the quotient when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1
Answer by CharlesG2(834) (Show Source):
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use long division to find the quotient when 2x^5+4x^4-x^3-x^2+7 is divided by 2x^2-1

synthetic division
..............x^3 + 2x^2 + (1/2)
2x^2 - 1 --> 2x^5 + 4x^4 - x^3 - x^2 + 0x + 7
.............2x^5 + 0x^4 - x^3
....................4x^4 + 0x^3 - x^2
....................4x^4 + 0x^3 - 2x^2
...................................x^2 + 0x + 7
...................................x^2 + 0x - (1/2)
............................................(15/2)

x^3 + 2x^2 + (1/2) + 15/(2 * (2x^2 - 1))
x^3 + 2x^2 + (1/2) + 15/(4x^2 - 2)
check:
(2x^2 - 1)(x^3 + 2x^2 + (1/2) + 15/(4x^2 - 2))
x^3(2x^2 - 1) + 2x^2(2x^2 - 1) + (1/2)(2x^2 - 1) + (15/(4x^2 - 2))(2x^2 - 1)
2x^5 - x^3 + 4x^4 - 2x^2 + x^2 - (1/2) + (15/2)
2x^5 + 4x^4 - x^3 - x^2 + (14/2)
2x^5 + 4x^4 - x^3 - x^2 + 7, yes