Use synthetic division to solve (x4 – 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 (x4 – 1) ÷ (x – 1), the quotient we get is x3 + x2 + x + 1.
We use synthetic division of a polynomial when the divisor is a linear factor. Let's solve this step by step.
= (x4 – 1) ÷ (x – 1) ⇒ (x4 – 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.
Hence, after using the synthetic division of (x4 – 1) ÷ (x – 1), the quotient we get is x3 + x2 + x + 1.
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