The polynomial y^3+y^2+my-7 has the same remainder when it is divided by either y-1 or y+1. What is the remainder?

First we have to find the value of m, the only solution possible is with y values -1 and 1 respectively so that it is divided by either y-1 or y+1

1*3+1*2+1*m -7 = (-1)*3+(-1)*2+(-1)*m -7

m= -1

Now let's find the reminder: y^3+ y^2 -y -7 / y-1 = -6

and y^3+ y^2 -y -7 / y+1 = -6

Answer: Reminder = -6

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