Question

(x^2-x+1) is a factor of the polynomial

(a) x^4+1
(b) x^4-1
(c) x^3-1
(d) x^3+1​

Answer 1

x³–1 is the answer because

x³– 1³ by using Identity a³-b³ = (a-b)(a²-ab+b²)

= (x – 1)[(x)² - (x)(1) + (1)²]

= (x – 1)(x²- x + 1)

Hence, x²- x + 1 is a factor of x³-1

I hope it helps you.