Is x^5 - 5x^4 + 4x^3 - 3x^2 + 2x + 1 a polynomial

yes

Step-by-step explanation:

Polynomial Long Division:

4.3 Polynomial Long Division

Dividing : x5-5x4+10x3-10x2+5x-1

("Dividend")

By : x-1 ("Divisor")

dividend x5 - 5x4 + 10x3 - 10x2 + 5x - 1

- divisor * x4 x5 - x4

remainder - 4x4 + 10x3 - 10x2 + 5x - 1

- divisor * - 4x3 - 4x4 + 4x3

remainder 6x3 - 10x2 + 5x - 1

- divisor * 6x2 6x3 - 6x2

remainder - 4x2 + 5x - 1

- divisor * - 4x1 - 4x2 + 4x

remainder x - 1

- divisor * x0 x - 1

remainder 0

Quotient : x4-4x3+6x2-4x+1 Remainder: 0