Q: Use polynomial long division to divide: x²/(1-3x)
A: OK… Trying to format this to look like a long division problem:
-3x + 1 | x²
(1) Ask yourself: how many times does -3x go into x²? The answer is -(1/3)x, so we put that above:
………. -(1/3)x
-3x + 1 | x²
Now, we multiply -(1/3)x by -3x + 1 and bring it down like so:
………. -(1/3)x
-3x + 1 | x²
………….x² – (1/3)x
OK, now we subtract red from red to get blue:
………. -(1/3)x
-3x + 1 | x²
…………1(x² – (1/3)x)
………………….. (1/3)x
Now we ask ourselves: How many times does -3x go into (1/3)x… The answer to that is -(1/9) times:
………. -(1/3)x – (1/9)
-3x + 1 | x²
…………1(x² – (1/3)x)
………………….. (1/3)x
Now, multiply -1/9 times -3x + 1 and bring down like so to get blue:
………. -(1/3)x – (1/9)
-3x + 1 | x²
…………1(x² – (1/3)x)
…………………….. (1/3)x
……………………..1/3x – 1/9
Subtract blue from blue to get purple:
………. -(1/3)x – (1/9)
-3x + 1 | x²
…………1(x² – (1/3)x)
…………………….. (1/3)x
……………………..-(1/3x – 1/9)
………………………………….1/9
And, we stop because -3x cannot go into 1/9…
So,
x²/(1-3x) = -(1/3)x – (1/9) + (1/9)/(-3x + 1) = -1/3x – 1/9 + 1/(-27x + 9).
thank you so very much or all your help
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