Due to the reminder Theorem P(1) and P(-1) will give the reminders of dividing by x-1 and x+1 respectively
For the polynomial to have the same reminder when divided by either (y-1) or (y+1) you need to make P(1) = P(-1) and solve for m:
1^3+1^2+1*m -7 = (-1)^3+(-1)^2+(-1)*m -7
1+1+m-7 = -1+1-m -7
2m = -2
m = -1
Now to find the actual reminder in both cases we have to put the value of m that we just found into the polynomial.
We will get: y^3+ y^2 + (-1)y -7 = y^3+ y^2 -y -7
Now let's divide it by y+1 and y-1
y^3+ y^2 -y -7 / y-1 = -6 and same answer is for y^3+ y^2 -y -7/y+1 = -6
If you will just divide y^3+ y^2 +my -7/y-1 or y^3+ y^2 -y -7/y+1 you will get ( -m-7 ) in both cases and if you use above mentioned Polynomial Remainder Theorem and method to find the value of m, you will get -(-1) -7 = -6.
Hope this explains it.
Let me know if you have any questions or if you would want me to explain any of this even in more detail.
Apr 21st, 2015
Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.