# Use synthetic division to solve (x^{4} – 1) ÷ (x – 1). What is the quotient?

We will be using the concept of synthetic division to answer this question.

### Answer: After using the synthetic division of (x^{4} – 1) ÷ (x – 1), the quotient we get is x^{3} + x^{2} + x + 1.

We use synthetic division of a polynomial when the divisor is a linear factor. Let's solve this step by step.

**Explanation:**

Given:

= (x^{4} – 1) ÷ (x – 1) ⇒ (x^{4} – 1) / (x – 1)

- Arrange the terms of the polynomial is in the standard form.
- Write only the coefficients in the dividend's place.
- Write the zero of the linear factor in the divisor's place. Here it is 1.
- Bring the first coefficient down.
- Multiply it with the divisor and write it below the next coefficient.
- Add them and write the value below.
- Repeat the previous 2 steps until you reach the last term.
- Separate the last term thus obtained which is the remainder.
- Now group the coefficients with the variables to get the quotient.

We can calculate the quotient and remainder using Cuemath's Synthetic Division Calculator.

### Hence, after using the synthetic division of (x^{4} – 1) ÷ (x – 1), the quotient we get is x^{3} + x^{2} + x + 1.

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