Explanation Given information: The polynomial is x 3 − x 2 − 30 x . Formula used: Steps for factorization a trinomial by a c -Method are: Step 1: Factor out the greatest common factor, if any. Write the resultant trinomial as a x 2 + b x + c . Step 2: Multiply the coefficient of x 2 and the constant term c . Step 3: Determine p and q , the factors of the product a c , such that p q = a c and p + q = b . Step 4: Write the middle term, b, as the sum of the factors obtained in step (3). Step 4: Factor the expression be grouping. Step 5: Check the result by multiplying the factors obtained in step (4). Calculation: Consider the provided expression x 3 − x 2 − 30 x . The common factor of the polynomial is x . Factor out the common factor x as follows: x 3 − x 2 − 30 x = x ( x 2 − x − 30 ) Factorize the polynomial x 2 − x − 30 using the a c -Method as follows: Multiply the coefficient of x 2 that is 1 and the constant term − 30 , 1 × ( − 30 ) = − 30 Since, the coefficient of x is negative and product of coefficient of x 2 and constant term is also negative. So, select a positive and negative factor of − 30 . Thus, the possible negative factors of − 30 and their sum is as follows: Pairs of factors Sum of factors 1 × ( − 30 ) 1 + ( − 30 ) = − 29 2 × ( − 15 ) 2 + ( − 15 ) = − 13 3 × ( − 10 ) 3 + ( − 10 ) = − 7 5 × ( − 6 ) 5 + ( − 6 ) = − 1 Now arrange the factors of − 30 in a way that their sum will give the coefficient of x that is − 1 in the polynomial x 2 − x − 30 . The product of 5 and − 6 is − 30 and the sum of 5 + ( − 6 ) is − 1

9th Edition

ISBN: 9780321997173

Author: Marvin L. Bittinger, Judith A. Beecher

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 11, Problem 19RE

To determine

To calculate: The factorization of the polynomial x3−x2−30x.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 18RE

Chapter 11, Problem 20RE

Students have asked these similar questions

Q5: Discuss the stability critical point of the ODEs x + (*)² + 2x² = 2 and draw the phase portrait. (10M)

A retail store manager claims that the average daily sales of the store are $1,500. You aim to test whether the actual average daily sales differ significantly from this claimed value. You can provide your answer by inserting a text box and the answer must include: Null hypothesis, Alternative hypothesis, Show answer (output table/summary table), and Conclusion based on the P value. Showing the calculation is a must. If calculation is missing,so please provide a step by step on the answers Numerical answers in the yellow cells

. The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.What is the probability of the union of being either a freshman or senior? 0.07 0.44 0.50 0.25

Chapter 11 Solutions

Developmental Mathematics (9th Edition)

Ch. 11.1 - Objective 7.7d: Use the distributive laws to...Ch. 11.1 - Prob. 2SR Ch. 11.1 - Prob. 1DE Ch. 11.1 - Prob. 2DE Ch. 11.1 - Prob. 3DE Ch. 11.1 - Prob. 4DE Ch. 11.1 - Prob. 5DE Ch. 11.1 - Prob. 6DE Ch. 11.1 - Find the GCF. GS 24m5n6,12mn3,16m2n2,8m4n4 The...Ch. 11.1 - Prob. 8DE

Knowledge Booster

Learn more about

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

The factorization of the polynomial x 3 − x 2 − 30 x .

Solution Summary: The author explains how to calculate the factorization of the polynomial x3-X2-30x.

Videos

To calculate: The factorization of the polynomial x3−x2−30x.

Want to see the full answer?

Chapter 11 Solutions