Question

If f(x)=x^5-x^2, then what is the remainder when f(x) is divided by x+1

Answer 1

It’s very simple
Equate the x+ 1 = 0
So x= -1
Put -1 into x^5 - x^2
So f(-1)= (-1)^5 - (-1)^2
= -2
It hope it helped :)
This is the simplest way of getting the remainder. So the reminder is -2

Answer 2

Answer: -2

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Reason:

We'll use the remainder theorem. When dividing the polynomial function p(x) by x-k, the remainder is p(k).

Comparing x+1 to x-k, we see that k = -1. It might help to think of x+1 as x-(-1).

Plug this k value into the function to find the remainder when dividing by x+1.

So,

f(x) = x^5-x^2

f(-1) = (-1)^5 - (-1)^2

f(-1) = -1 - 1

f(-1) = -2

The remainder is -2

This can be confirmed through use of either synthetic division or polynomial long division as shown in the diagrams below. Synthetic division is the better option in my opinion.