Explanation Given information: The provided expression is ( 6 x 3 − 5 x 2 − 13 x + 13 ) ÷ ( 2 x + 3 ) . Formula used: To divide a polynomial by a binomial use the long division method, multiply the divisor by the variable such that it cancels out until the degree of remainder is less than degree of divisor. Calculation: Consider the expression, ( 6 x 3 − 5 x 2 − 13 x + 13 ) ÷ ( 2 x + 3 ) . Rewrite the expression as, ( 6 x 3 − 5 x 2 − 13 x + 13 ) ( 2 x + 3 ) Find the first term of quotient by dividing first term of dividend by first term of divisior: 6 x 3 2 x = 3 x 2 Now, multiply ( 2 x + 3 ) by 3 x 2 , change the sign of the monomials, combine the like terms and subtract them: ( 2 x + 3 ) 3 x 2 6 x 3 − 5 x 2 − 13 x + 13 − ( 6 x 3 + 9 x 2 ) _ − 14 x 2 − 13 x + 13 Find second term of quotient by dividing first term of new dividend by first term of divisor: − 14 x 2 2 x = − 7 x Now, multiply ( 2 x + 3 ) by − 7 x , change the sign of the monomials, combine the like terms and add them: ( 2 x + 3 ) 3 x 2 − 7 x 6 x 3 − 5 x 2 − 13 x + 13 − ( 6 x 3 + 9 x 2 ) _ − 14 x 2 − 13 x + 13 − ( − 14 x 2 − 21 x ) _ 8 x + 13 Find third term of the quotient by dividing first term of new dividend by first term of divisor: 8 x 2 x = 4 Now, multiply ( 2 x + 3 ) by 4 x , change the sign of the monomials, combine the like terms and add them: ( 2 x + 3 ) 3 x 2 − 7 x 6 x 3 − 5 x 2 − 13 x + 13

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

7th Edition

ISBN: 9780134462707

Author: Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

Publisher: PEARSON

See similar textbooks

Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Videos

Question

Chapter 4, Problem 71RE

To determine

To calculate: The value of the division of the expression (6x3−5x2−13x+13)÷(2x+3).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 70RE

Chapter 4, Problem 72RE

Chapter 4 Solutions

Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)

Ch. 4.1 - Multiply and simplify: x5xx4 Ch. 4.1 - Divide and simplify: (x+p)6(x+p).Ch. 4.1 - Simplify: 990.Ch. 4.1 - 4. Simplify: . Ch. 4.1 - 5. Simplify: . Ch. 4.1 - Simplify: (3a3)2.Ch. 4.1 - Each of the following statements is an example of...Ch. 4.1 - Each of the following statements is an example of...Ch. 4.1 - Prob. 3CYU Ch. 4.1 - Each of the following statements is an example of...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The value of the division of the expression ( 6 x 3 − 5 x 2 − 13 x + 13 ) ÷ ( 2 x + 3 ) .

Solution Summary: The author explains how to calculate the value of the division of a polynomial using the long division method.

Concept explainers

Videos

To calculate: The value of the division of the expression (6x3−5x2−13x+13)÷(2x+3).

Want to see the full answer?

Chapter 4 Solutions