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 8 ( b 3 ) 2 + 31 ( b 3 ) − 4 as follows. It is observed that, the coefficients are a = 8 , b = 31 and c = − 4 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 8 ( − 4 ) = − 32 Thus, the value of a c is –32. Step 2: Find the two number, e and f, whose product is a c = − 32 and whose sum is b = 31 . Obtain the list of integer factors of –32 such that product is –32 and sum is 31 as shown below in Table 1. Integers whose product is –32 1 , − 32 − 1 , 32 − 16 , 2 16 , − 2 Sum –31 31 –14 14 Table 1 From Table 1, it is observed that the numbers whose product is –32 and sum is 31 are − 1 and 32 . Let, the integers take the variables e = − 1 and f = 32 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c . Rewrite the expression 8 ( b 3 ) 2 + 31 ( b 3 ) − 4 in the form a ( b 3 ) 2 + e ( b 3 ) + f ( b 3 ) + c as, 8 ( b 3 ) 2 + 31 ( b 3 ) − 4 = 8 ( b 3 ) 2 − b 3 + 32 b 3 − 4 Step 4: Factor the expression in step 3 by grouping

11th Edition

ISBN: 9780134508290

Author: Evans

Publisher: PEARSON CUSTOM PUB.(CONSIGNMENT)

See similar textbooks

Videos

Question

Chapter 6.2, Problem 41E

To determine

To factor: The expression 8b6+31b3−4 completely.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.2, Problem 40E

Chapter 6.2, Problem 42E

Students have asked these similar questions

A researcher wishes to estimate, with 90% confidence, the population proportion of adults who support labeling legislation for genetically modified organisms (GMOs). Her estimate must be accurate within 4% of the true proportion. (a) No preliminary estimate is available. Find the minimum sample size needed. (b) Find the minimum sample size needed, using a prior study that found that 65% of the respondents said they support labeling legislation for GMOs. (c) Compare the results from parts (a) and (b). ... (a) What is the minimum sample size needed assuming that no prior information is available? n = (Round up to the nearest whole number as needed.)

The table available below shows the costs per mile (in cents) for a sample of automobiles. At a = 0.05, can you conclude that at least one mean cost per mile is different from the others? Click on the icon to view the data table. Let Hss, HMS, HLS, Hsuv and Hмy represent the mean costs per mile for small sedans, medium sedans, large sedans, SUV 4WDs, and minivans respectively. What are the hypotheses for this test? OA. Ho: Not all the means are equal. Ha Hss HMS HLS HSUV HMV B. Ho Hss HMS HLS HSUV = μMV Ha: Hss *HMS *HLS*HSUV * HMV C. Ho Hss HMS HLS HSUV =μMV = = H: Not all the means are equal. D. Ho Hss HMS HLS HSUV HMV Ha Hss HMS HLS =HSUV = HMV

Question: A company launches two different marketing campaigns to promote the same product in two different regions. After one month, the company collects the sales data (in units sold) from both regions to compare the effectiveness of the campaigns. The company wants to determine whether there is a significant difference in the mean sales between the two regions. Perform a two sample T-test 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. (2 points = 0.5 x 4 Answers) Each of these is worth 0.5 points. However, showing the calculation is must. If calculation is missing, the whole answer won't get any credit.

Chapter 6 Solutions

EBK 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 8 b 6 + 31 b 3 − 4 completely.

Videos

To factor: The expression 8b6+31b3−4 completely.

Want to see the full answer?

Chapter 6 Solutions