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Use synthetic division to divide x³+4x² - 13x-20 by x - 3 The quotient is: The remainder is: -13 -20

Use synthetic division to divide x³+4x² - 13x-20 by x - 3 The quotient is: The remainder is: -13 -20

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Synthetic Division Method Explanation **Objective:** Use synthetic division to divide \( x^3 + 4x^2 - 13x - 20 \) by \( x - 3 \). #### Steps: 1. **Setup the Synthetic Division:** - Write down the coefficients of the polynomial \( x^3 + 4x^2 - 13x - 20 \). - Coefficients: \( 1, 4, -13, -20 \) - The divisor \( x-3 \) gives us a value of \( 3 \) (we take \( x- 3 = 0 \) which results in \( x = 3 \)). 2. **Arrange in Synthetic Division Format:** - Write \( 3 \) on the left-hand side. - Write the coefficients \( 1, 4, -13, -20 \) on the right-hand side in a row. 3. **Perform the Division:** - Draw a horizontal line below the coefficients and a vertical line separating the divisor \( 3 \) from the coefficients. - Bring down the first coefficient (1). - Multiply the number brought down by the divisor \( 3 \). - Write the product under the next coefficient and add. - Repeat the process for the remaining coefficients. #### Visual Representation: \[ \begin{array}{r|rrrr} 3 & 1 & 4 & -13 & -20 \\ & & 3 & 21 & 24 \\ \hline & 1 & 7 & 8 & 4 \\ \end{array} \] #### Explanation of Steps in the Diagram: - The first coefficient (1) is brought down unchanged. - Next, multiply \( 1 \) (brought down) by \( 3 \) (divisor) to get \( 3 \). - Add \( 3 \) to \( 4 \), resulting in \( 7 \). - Multiply \( 7 \) by \( 3 \) to get \( 21 \). - Add \( 21 \) to \( -13 \), resulting in \( 8 \). - Multiply \( 8 \) by \( 3 \) to get \( 24 \). - Add \( 24 \) to \( -20 \), resulting
Transcribed Image Text:### Synthetic Division Method Explanation **Objective:** Use synthetic division to divide \( x^3 + 4x^2 - 13x - 20 \) by \( x - 3 \). #### Steps: 1. **Setup the Synthetic Division:** - Write down the coefficients of the polynomial \( x^3 + 4x^2 - 13x - 20 \). - Coefficients: \( 1, 4, -13, -20 \) - The divisor \( x-3 \) gives us a value of \( 3 \) (we take \( x- 3 = 0 \) which results in \( x = 3 \)). 2. **Arrange in Synthetic Division Format:** - Write \( 3 \) on the left-hand side. - Write the coefficients \( 1, 4, -13, -20 \) on the right-hand side in a row. 3. **Perform the Division:** - Draw a horizontal line below the coefficients and a vertical line separating the divisor \( 3 \) from the coefficients. - Bring down the first coefficient (1). - Multiply the number brought down by the divisor \( 3 \). - Write the product under the next coefficient and add. - Repeat the process for the remaining coefficients. #### Visual Representation: \[ \begin{array}{r|rrrr} 3 & 1 & 4 & -13 & -20 \\ & & 3 & 21 & 24 \\ \hline & 1 & 7 & 8 & 4 \\ \end{array} \] #### Explanation of Steps in the Diagram: - The first coefficient (1) is brought down unchanged. - Next, multiply \( 1 \) (brought down) by \( 3 \) (divisor) to get \( 3 \). - Add \( 3 \) to \( 4 \), resulting in \( 7 \). - Multiply \( 7 \) by \( 3 \) to get \( 21 \). - Add \( 21 \) to \( -13 \), resulting in \( 8 \). - Multiply \( 8 \) by \( 3 \) to get \( 24 \). - Add \( 24 \) to \( -20 \), resulting
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