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2x-1 ) 2x^3+5x^2+17x+4
Take the leading term of the divisor, 2x in this case, and divide it into the leading term of the dividend, 2x^3 in this case. 2x^3 / 2x = x^2, and that is the first term of our quotient.
x^2
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2x-1 ) 2x^3+5x^2+17x+4
- ( 2x^3-x^2)
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6x^2+17x+4
Multiply (2x-1) by x^2 and subtract as shown above.
Now take the leading term of this new polynomial and divide it by 2x. That yields 3x. Use 3x as the next term of your quotient and repeat this process.
x^2+3x
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2x-1 ) 2x^3+5x^2+17x+4
- ( 2x^3-x^2)
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6x^2+17x+4
- (6x^2 -3x)
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20x+4
20x / 2x = 10, so use 10 as the next part of the quotient:
x^2 +3x + 10
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2x-1 ) 2x^3+5x^2+17x+4
- ( 2x^3 -x^2)
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6x^2+17x+4
- (6x^2 -3x)
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20x +4
-(20x-10)
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14
Since 14<2x, the division is over. 14 is the remainder.
So the final answer is:
x^2 + 3x + 10 + [14/(2x-1)].
