Questions: Use synthetic division to perform the division. x^5-1 / x-1 x^5-1 / x-1 =

Use synthetic division to perform the division. x^5-1 / x-1 x^5-1 / x-1 =
Transcript text: Use synthetic division to perform the division. \[ \begin{array}{l} \frac{x^{5}-1}{x-1} \\ \frac{x^{5}-1}{x-1}= \end{array} \]
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Solution

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Solution Steps

Step 1: Write down the coefficients of the polynomial in descending order of power.

The coefficients are: [1, 0, 0, 0, 0, -1]

Step 2: Change the sign of 'a' from the divisor and place it to the left side.

The divisor is \(x + (1)\).

Step 3: Bring down the leading coefficient as is to the row below.
Steps 4, 5, 6: Perform the synthetic division.
Step 7: Interpret the result.

Final Answer:

The quotient polynomial is: x^5 + x^4 + x^3 + x^2 + x^1

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