Skip to main content
Ch. 3 - Polynomial and Rational Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 3 - Polynomial and Rational FunctionsProblem 11
Chapter 4, Problem 11

Use synthetic division to perform each division. (x4 + 4x3 + 2x2 + 9x+4) / x+4

Verified step by step guidance
1
Identify the divisor and rewrite it in the form \(x - c\). Since the divisor is \(x + 4\), rewrite it as \(x - (-4)\), so \(c = -4\).
Write down the coefficients of the dividend polynomial \(x^4 + 4x^3 + 2x^2 + 9x + 4\). These are: 1, 4, 2, 9, and 4.
Set up the synthetic division tableau by placing \(c = -4\) to the left and the coefficients in a row: 1, 4, 2, 9, 4.
Perform synthetic division by bringing down the first coefficient (1), then multiply it by \(c\) (-4), add the result to the next coefficient, and repeat this process across all coefficients.
Interpret the final row of numbers: the first four numbers represent the coefficients of the quotient polynomial (starting from degree 3), and the last number is the remainder.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
7m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Synthetic Division

Synthetic division is a shortcut method for dividing a polynomial by a linear binomial of the form x - c. It simplifies the long division process by using only the coefficients of the polynomial and performing arithmetic operations in a tabular form. This method is efficient for finding quotients and remainders quickly.
Recommended video:
05:10
Higher Powers of i

Polynomial Coefficients and Setup

To use synthetic division, you must identify and list the coefficients of the dividend polynomial in descending order of degree. If any terms are missing, their coefficients are represented as zero. Proper setup ensures accurate calculations during the synthetic division process.
Recommended video:
Guided course
05:16
Standard Form of Polynomials

Interpreting the Divisor in Synthetic Division

In synthetic division, the divisor x + 4 is rewritten as x - (-4), so the value used in the process is -4. Recognizing this sign change is crucial because synthetic division uses the root of the divisor (the value that makes it zero) to perform the calculations correctly.
Recommended video:
2:57
Probability of Non-Mutually Exclusive Events Example
Related Practice
Textbook Question

Solve each problem. If y varies inversely as x, and y=10 when x=3, find y when x=20.

5
views
Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation.

(a) -(x + 1)(x + 2) ≥ 0

(b) -(x + 1)(x + 2) > 0

(c) -(x + 1)(x + 2) ≤ 0

(d) -(x + 1)(x + 2) < 0

Textbook Question

Use the factor theorem and synthetic division to determine whether the second polynomial is a factor of the first. See Example 1.

x3+6x2−2x−7;x+1x^3+6x^2-2x-7; x+1

Textbook Question

Solve each quadratic inequality. Give the solution set in interval notation.

(a) (x - 5)(x + 2) ≥ 0

(b) (x - 5)(x + 2) > 0

(c) (x - 5)(x + 2) ≤ 0

(d) (x - 5)(x + 2) < 0

Textbook Question

Consider the graph of each quadratic function.

a) Give the domain and range.

Textbook Question

Use synthetic division to perform each division. (3x3+6x2-8x+3)/(x+3)

2
views