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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.
Explanation:
Given:
= (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.
We can calculate the quotient and remainder using Cuemath's Synthetic Division Calculator.
Hence, after using the synthetic division of (x4 – 1) ÷ (x – 1), the quotient we get is x3 + x2 + x + 1.
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