what number multiplied by y gets you 3y^3? The answer is 3y^2. Place 3y^2 over 3y^3. Now multiply 3y^2 and y and place it underneath 3y^3. Multiply 3y^2 by 1 and place it under y^2
_3y^2___________________
Y+1 |3y^3 + y^2
3y^3 + 3y^2
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Now subtract the second line from the first
_3y^2___________________
Y+1 |3y^3 + y^2
-(3y^3 + 3y^2)
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-2y^2
Now what value multiplied by y gives you -2y^2? This value is -2y, so place it over y^2. Now multiply -2y by (y+1) and place that product under -2y^2+0y and subtract the lines.
_3y^2_-_2y_________________
Y+1 |3y^3 + y^2 + 0y + 0
-(3y^3 + 3y^2)
----------------
-2y^2 + 0y
-(2y^2 - 2y)
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2y
Now what value multiplied by y gives you 2y? This value is 2, so place it over 0y. Now multiply 2 by (y+1) and place that product under 2y+0 and subtract the lines.
_3y^2_-_2y__+__2_____________
Y+1 |3y^3 + y^2 + 0y + 0
-(3y^3 + 3y^2)
----------------
-2y^2 + 0y
-(2y^2 - 2y)
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2y + 0
-(2y + 2)
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-2
So the answer is:
Or the answer in remainder format is:
3y^2 - 2y + 2 R -2
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