Explanation Procedure used: Factoring general trinomials by grouping : In a trinomial of the form a x 2 + b x + c , a ≠ 1 , split up the x -term into two terms using the method described below. “Step 1: Find the product a c . Step 2: Find two numbers whose product is a c and whose sums is b . Step 3: Replace the middle term bx with two x -terms having these numbers as coefficients. That is, a x 2 + b x + c = a x 2 + m x + n x + c . Step 4: Complete the factorization by grouping”. Calculation: Factor the given expression x 2 − 4 x − 45 as follows. It is observed that, the coefficients are a = 1 , b = − 4 and c = − 45 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 1 ( − 45 ) = − 45 Thus, the value of a c is –45. Step 2: Find the two number, e and f, whose product is a c = − 45 and whose sum is b = − 4 . Obtain the list of integer factors of –45 such that product is –45 and sum is –4 as shown below in Table 1. Integers whose product is –45 1 , − 45 − 1 , 45 − 9 , 5 9 , − 5 Sum –44 44 –4 4 Table 1 From the Table 1, it is observed that the numbers whose product is –45 and sum is –4 are − 9 and 5 . Let, the integers take the variables e = − 9 and f = 5

11th Edition

ISBN: 9780134437705

Author: Washington

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 6, Problem 28RE

To determine

To factor: The expression x2−4x−45 completely.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 27RE

Chapter 6, Problem 29RE

Students have asked these similar questions

Please explain this theorem and proof

Please answer number 17

Nicole organized a new corporation. The corporation began business on April 1 of year 1. She made the following expenditures associated with getting the corporation started: Expense Date Amount Attorney fees for articles of incorporation February 10 $ 40,500 March 1-March 30 wages March 30 6,550 March 1-March 30 rent Stock issuance costs March 30 2,850 April 1-May 30 wages Note: Leave no answer blank. Enter zero if applicable. April 1 May 30 24,000 16,375 c. What amount can the corporation deduct as amortization expense for the organizational expenditures and for the start-up costs for year 1 [not including the amount determined in part (b)]? Note: Round intermediate calculations to 2 decimal places and final answer to the nearest whole dollar amount. Start-up costs amortized Organizational expenditures amortized

Chapter 6 Solutions

Basic Technical Mathematics

Ch. 6.1 - Prob. 1PE Ch. 6.1 - Prob. 2PE Ch. 6.1 - Prob. 3PE Ch. 6.1 - Prob. 4PE Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E

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.

To factor: The expression x 2 − 4 x − 45 completely.

Concept explainers

Videos

To factor: The expression x2−4x−45 completely.

Want to see the full answer?

Chapter 6 Solutions