Title: Polynomial Division Techniques---**Objective:**Learn how to use long division or synthetic division to divide polynomials.**Problem:**Divide the polynomial \( x^3 - 2x^2 + x - 5 \) by \( x - 1 \).---**Instructions:**1. **Long Division Method:** - Write the dividend \( x^3 - 2x^2 + x - 5 \) and the divisor \( x - 1 \). - Divide the first term of the dividend by the first term of the divisor. - Multiply the entire divisor by the result and subtract from the current dividend. - Repeat the process with the new polynomial formed after subtraction until no terms are left.2. **Synthetic Division Method:** - Use the zero of the divisor \( x - 1 \), which is 1. - List the coefficients of the dividend: 1, -2, 1, -5. - Bring down the leading coefficient to start the process. - Multiply the divisor root by the number brought down and add it to the next coefficient. - Continue through all coefficients. - The last number is the remainder.These methods will provide the quotient of the polynomial division, with any remainder. Practice using both to understand the process thoroughly.

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Answered: Use long division or synthetic division…

Math

Trigonometry

Use long division or synthetic division to divide the following polynomials: x³2x²+x-5÷x-1

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Question

Title: Polynomial Division Techniques

---

**Objective:**

Learn how to use long division or synthetic division to divide polynomials.

**Problem:**

Divide the polynomial \( x^3 - 2x^2 + x - 5 \) by \( x - 1 \).

---

**Instructions:**

1. **Long Division Method:**
- Write the dividend \( x^3 - 2x^2 + x - 5 \) and the divisor \( x - 1 \).
- Divide the first term of the dividend by the first term of the divisor.
- Multiply the entire divisor by the result and subtract from the current dividend.
- Repeat the process with the new polynomial formed after subtraction until no terms are left.

2. **Synthetic Division Method:**
- Use the zero of the divisor \( x - 1 \), which is 1.
- List the coefficients of the dividend: 1, -2, 1, -5.
- Bring down the leading coefficient to start the process.
- Multiply the divisor root by the number brought down and add it to the next coefficient.
- Continue through all coefficients.
- The last number is the remainder.

These methods will provide the quotient of the polynomial division, with any remainder. Practice using both to understand the process thoroughly.

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