Math help needed please,Use the remainder theorem to determine the remainder (x^4-4x+1)/(x+1)?

Question

Your help is appreciated thank you!

Please explain each step as you go along

Answer 1

Assuming that your polynomial is p(x) = x^4 - 4x + 1 and that you are dividing it by x + 1 then you just find p(-1)

p(-1) = -1^4 - 4.-1 + 1 = 6

If you had been dividing by x - 3 you would find p(3)

The only other possibility is that you have to show the long division method. The # should be ignored

##### x^3
------------------------------------
x + 1 ) x^4 +0x^3 +0x^2 - 4x + 1 by dividing x into x^4
##### x^4 + x^3
---------------
######### -x^3 subtracting the two rows

Now divide by x again and continue like this

Answer 2

X^4 -4x + 1 = (x +1)f(x) +Remainder
Setting x=-1 both sides of the equation gives RHS = remainder as x+1 now = 0 so (x+1)(f(x) = 0 so L.H.S. must also = Remainder

As previous people have said 6

Answer 3

f(x) = (x^4-4x+1)

remainder = f(-1) = 6

Answer 4

your teacher is cruel