The degree of the remainder is at most 1 since we’re dividing by a degree 2 polynomial. So the remainder takes the form ax+b. We just need to work out a and b.

When we do the division, since ax+b is the remainder, we get

x^2020 + x^1947 + 1 = ( x² – 1 ) g(x) + ax + b.

Since x² – 1 vanishes when we put x = 1 and x = -1, we put these values in:

## Answers ( )

Answer:x + 2

Step-by-step explanation:The degree of the remainder is at most 1 since we’re dividing by a degree 2 polynomial. So the remainder takes the form ax+b. We just need to work out a and b.

When we do the division, since ax+b is the remainder, we get

x^2020 + x^1947 + 1 = ( x² – 1 ) g(x) + ax + b.

Since x² – 1 vanishes when we put x = 1 and x = -1, we put these values in:

Putting x = 1 gives 3 = a + b. (*)

Putting x = -1 gives 1 = -a + b. (**)

Subtracting (**) from (*) gives 2a = 2, so a = 1.

Adding (*) and (**) gives 2b = 4, so b = 2.

Therefore the remainder is ax+b = x+2.

Hope this helps.