Respuesta :

Answer:

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....