Question

Use synthetic division to solve (x4 – 1) ÷ (x – 1). What is the quotient? x cubed minus x squared x minus 1 x3 x cubed x squared x 1 x3 – 2.

Answer 1

The quotient is $\rm x^2+x+1$.

Given

Use synthetic division to solve (x4 – 1) ÷ (x – 1).

What is synthetic division?

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Therefore,

The quotient is;

$\rm =\dfrac{x^3-1}{x-1}\\\\=\dfrac{x^3+x^2+x-x^2-x-1}{x-1}\\\\ \rm\rm =\dfrac{x(x^2+x+1)-1(x^2+x+1)}{x-1}\\\\= \dfrac{(x-1)(x^2+x+1)}{x-1}\\\\= x^2+x+1$

Hence, the quotient is $\rm x^2+x+1$.

To know more about Synthetic division click the link given below.

brainly.com/question/25997349