Use synthetic division to solve (x4 - 1) = (x - 1). What is the quotient?

x3 - x2+x-1

O x3

x+x2+x+1

x3-2

x3 - 3x + 1

The quotient is x³+x²+x+1

Step-by-step explanation:

= (x^4-1) : (x-1)

= (x^4-1) / (x-1)

Solve the numerator by using perfect square formula:

⇒x^4-1 = (x²-1) (x²+1)

= (x²-1) (x²+1) / (x-1)

Further solve the numerator by using perfect square formula:

= (x+1) (x-1) (x²+1) / (x-1)

Cancel the like terms of numerator and denominator

We get;

= (x+1) (x²+1)

Multiply the terms:

=x³+x+x²+1

Re-arrange the terms:

=x³+x²+x+1

Hence the quotient is x³+x²+x+1 ...