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 4 a 2 x 2 + 26 a 2 x + 36 a 2 as follows. Rewrite the expression as, 4 a 2 x 2 + 26 a 2 x + 36 a 2 = 2 a 2 ( 2 x 2 + 13 x + 18 ) (1) Consider the expression 2 x 2 + 13 x + 18 . It is observed that, the coefficients are a = 2 , b = 13 and c = 18 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 2 ( 18 ) = 36 Thus, the value of a c is 36. Step 2: Find the two number, e and f, whose product is a c = 36 and whose sum is b = 13 . Obtain the list of integer factors of 36 such that product is 36 and sum is 13 as shown below in Table 1. Integers whose product is 36 1 , 36 − 1 , − 36 18 , 2 − 9 , − 4 9 , 4 − 18 , − 2 Sum 37 –37 20 –13 13 –20 Table 1 From Table 1, it is observed that the numbers whose product is 36 and sum is 13 are 9 and 4 . Let, the integers take the variables e = 4 and f = 9 . Step 3: Write a x 2 + b x + c = a x 2 + m x + n x + c

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, Problem 38RE

To determine

To factor: The expression 4a2x2+26a2x+36a2 completely.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 37RE

Chapter 6, Problem 39RE

Students have asked these similar questions

Introduce yourself and describe a time when you used data in a personal or professional decision. This could be anything from analyzing sales data on the job to making an informed purchasing decision about a home or car. Describe to Susan how to take a sample of the student population that would not represent the population well. Describe to Susan how to take a sample of the student population that would represent the population well. Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.

Answers

What is a solution to a differential equation? We said that a differential equation is an equation that describes the derivative, or derivatives, of a function that is unknown to us. By a solution to a differential equation, we mean simply a function that satisfies this description. 2. Here is a differential equation which describes an unknown position function s(t): ds dt 318 4t+1, ds (a) To check that s(t) = 2t2 + t is a solution to this differential equation, calculate you really do get 4t +1. and check that dt' (b) Is s(t) = 2t2 +++ 4 also a solution to this differential equation? (c) Is s(t)=2t2 + 3t also a solution to this differential equation? ds 1 dt (d) To find all possible solutions, start with the differential equation = 4t + 1, then move dt to the right side of the equation by multiplying, and then integrate both sides. What do you get? (e) Does this differential equation have a unique solution, or an infinite family of solutions?

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 4 a 2 x 2 + 26 a 2 x + 36 a 2 completely.

Videos

To factor: The expression 4a2x2+26a2x+36a2 completely.

Want to see the full answer?

Chapter 6 Solutions