Question

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

Answer 1

Quotient is: x^3+x^2+x+1

Explanation:

We need to solve (x^4-1) ÷ (x-1) using synthetic division.

In synthetic division we write the coefficients in decreasing order of their powers. We have x^4-1 that can be written as: 1x^4 + 0x^3 + 0x^2 + 0x -1

so our coefficients will be

1 0 0 0 -1

and for synthetic division, we take the constant term of divisor and change its sign.

We have x-1, constant term -1 so, our value will be 1.

The division is attached in the figure below.

Quotient is: x^3+x^2+x+1

Answer 2

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend until it reaches the rest.

The attached figure shows the quotient given by:

`x ^ 3 + x ^ 2 + x + 1`

Answer:

Quotient:
`x ^ 3 + x ^ 2 + x + 1`

See attached image