Inactive Tutor answered • 03/06/13
Tutor
New to Wyzant
x - 6
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2x+3 ) 2x2 - 9x - 20
-(2x2 + 3x)
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-12x - 20
-(-12x - 18)
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- 2
The solution is x - 6 - 2/(2x+3).
Inactive Tutor
And I apologize for the grammatical errors. I can't edit my comment to go back and fix them, only the original posting. I hope this helps you.
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03/06/13
Inactive Tutor
I wanted to put the answer in a formatted way first. Now I'll talk about how I did this problem.
First, I started by looking at 2x2. If I divide this first term by 2x, what do I get? That answer is x. So when I multiply x by 2x+3, I get the quantity 2x2 + 3x. Just like in long division, you subtract this product out, leaving -12x - 20. -12x goes into 2x -6 times. Multiply 2x+3 by -6 gives you -12x - 18, which you subtract out leaving -2. You can't go any further so the remainder is written in fractional form with the divisor as the denominator: -2/(2x+3). So you final answer is x - 6 - 2/(2x+3). This satisfies the question, as R has x to the 0th power and D has x to the 1st power, and has been expressed as Q + R/D... quotient plus remainder over divisor.
03/06/13