Hey! i've been working on these questions but I have no idea how to solve this one, could anybody help me? Thanks in advance!

1)

2)

3)

4)

Step-by-step explanation:

Part (1)

As we have to determine it by ourselves, this is the polynomial having a degree of 3. p(x) with a degree of 3 means that the highest degree/exponent of x should be 3.

Part (2)

This can be the polynomial having the factor x-1 because if we put:

x - 1 = 0 =>  x = 1 in the above polynomial, it gives us a result of zero which shows us that (x-1) "is" a factor of the polynomial.

Part (3)

This can be the polynomial for which p(0) = 4 and p(-1) = 0

Let's check:

So, this is the required polynomial determined by "myself".

Part (4):

This is the polynomial having a remainder 6 when divided by (x-2)

Let's check:

Let x - 2 = 0 => x = 2

Putting in the above polynomial

So, Proved that it has a remainder of 6 when divided by (x-2)