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 12 B 2 + 22 B H − 4 H 2 as follows. Rewrite the expression as, 12 B 2 + 22 B H − 4 H 2 = 2 ( 6 B 2 + 11 B H − 2 H 2 ) (1) Consider the expression 6 B 2 + ( 11 H ) B − 2 H 2 . It is observed that, the coefficients are a = 6 , b = 11 H and c = − 2 H 2 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 6 ( − 2 H 2 ) = − 12 H 2 Thus, the value of a c is − 12 H 2 . Step 2: Find the two number, e and f, whose product is a c = − 12 H 2 and whose sum is b = 7 . Obtain the list of integer factors of − 12 H 2 such that product is − 12 H 2 and sum is 11 H as shown below in Table 1. Integers whose product is − 12 H 2 H , − 12 H − H , 12 H 6 H , − 2 H − 6 H , 2 H Sum –11 H 11 H 4 H –4 H Table 1 From Table 1, it is observed that the numbers whose product is − 12 H 2 and sum is 11 H are − H and 12 H . Let the variables e = − H and f = 12 H

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780134434636

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6.2, Problem 50E

To determine

To factor: The expression 12B2+22BH−4H2 completely.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.2, Problem 49E

Chapter 6.2, Problem 51E

Students have asked these similar questions

2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1 Mark] (ii) Prove that if a set ECR2 is closed then every convergent sequence (x(n))nen in E has its limit in E, that is (x(n)) CE and x() x x = E. [5 Marks] (iii) which is located on the parabola x2 = = x x4, contains a subsequence that Give an example of an unbounded sequence (r(n)) nEN CR2 (2, 16) and such that x(i) converges to the limit x = (2, 16) and such that x(i) # x() for any i j. [4 Marks

1. (i) which are not. Identify which of the following subsets of R2 are open and (a) A = (1, 3) x (1,2) (b) B = (1,3) x {1,2} (c) C = AUB (ii) Provide a sketch and a brief explanation to each of your answers. [6 Marks] Give an example of a bounded set in R2 which is not open. (iii) [2 Marks] Give an example of an open set in R2 which is not bounded. [2 Marks]

sat Pie Joday) B rove: ABCB. Step 1 Statement D is the midpoint of AC ED FD ZEDAZFDC Reason Given 2 ADDC Select a Reason... A OBB hp B E F D C

Chapter 6 Solutions

Student Solutions Manual For Basic Technical Mathematics And Basic Technical Mathematics With Calculus

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 12 B 2 + 22 B H − 4 H 2 completely.

Videos

To factor: The expression 12B2+22BH−4H2 completely.

Want to see the full answer?

Chapter 6 Solutions