When divided by x^2 - 1, the polynomial P leaves a remainder of 5x - 7. What is the remainder when P is divided by x - 1?
#Polynomial task
last heart
solar sleetBOT
When divided by x^2 - 1, the polynomial P leaves a remainder of 5x - 7. What is ...
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close
- Feel free to nominate the person for helper of the week in #helper-nominations
dusty laurel
what is the factored version of x^2 - 1
last heart
(x-1)(x+1)
high fjord
When divided by x^2 - 1, the polynomial P leaves a remainder of 5x - 7. What is ...
Suppose the quotient is Q(x). Then:
P(x)/(x^2 - 1) = Q(x) + (5x - 7)/(x^2 - 1)
Let's multiply everything by (x + 1).
P(x)/(x - 1) = (x + 1)Q(x) + (5x - 7)/(x - 1)
Now, this still isn't done, because the last expression isn't simplified to the form where the numerator has a smaller degree than the denominator. So, do that, then you'll see the remainder.
last heart
But you can't simplify (5x-7)(x-1) further. Can you give a hint what needs to be done next?
dusty laurel
what
(5x-7)/(x-1)
what do you multiply (x-1) by to get rid of the x in the numerator
dusty laurel
since we dont want x in the remainder
high fjord
Yes, very good!