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How do you find the quotient of #(2y^4-3y^2+1)div(y-1)# using long division?

Answer 1

#2y^3+2y^2-y-1#

#" "" "2y^3+2y^2-y-1# #y-1|bar(cancel(2y^4)+0y^3-3y^2+0y+1)|# #" "" " cancel(2y^4)-2y^3 # #" "" "bar(0+cancel(2y^3)-3y^2+0y+1)# #" "" " 0+cancel(2y^3)-2y^2# #" "" "bar( 0+00 cancel(-1y^2)+0y+1)# #" "" " 0+00cancel(-1y^2)+y# #" "" "bar( 0+00+00cancel(-1y+1)# #" "" " 0+00+00cancel(-1y+1# #" "" "bar(................................)#

Note: The sign is changed (+ to - or - to +) when the term is multiplied with the term in the quotient.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.