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 9 x 2 + 7 x y − 2 y 2 as follows. Consider the expression 9 x 2 + ( 7 y ) x − 2 y 2 , where x is variable and y is constant. It is observed that, the coefficients are a = 9 , b = 7 y and c = − 2 y 2 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 9 ( − 2 y 2 ) = − 18 y 2 Thus, the value of a c is − 18 y 2 . Step 2: Find the two number, m and n, whose product is a c = − 18 y 2 and whose sum is b = 7 y . Obtain the list of integer factors of − 18 y 2 such that product is − 18 y 2 and sum is 7 y as shown below in Table 1. Integers whose product is − 18 y 2 y , − 18 y 2 y , − 9 y − 2 y , 9 y − 6 y , 3 y 6 y , − 3 y Sum –17 y –7 y 7 y –3 y 3 y Table 1 From Table 1, it is observed that the numbers whose product is − 18 y 2 and sum is 7 y are − 2 y and 9 y

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

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 6.2, Problem 33E

To determine

To factor: The given expression 9x2+7xy−2y2 completely.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.2, Problem 32E

Chapter 6.2, Problem 34E

Students have asked these similar questions

(b) In various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The full dataset is in the Minitab file coins.mwx. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and seven from the fourth coinage (variable Coin4) which was produced a number of years later. (For the purposes of this question, you can ignore the variables Coin2 and Coin3.) In particular, in Activity 8 and Exercise 2 of Computer Book B, it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel’s reign. You are about to investigate this question using a two-sample t-interval. (i) Using Minitab, find either the sample standard deviations of the two variables…

5. (a) State the Residue Theorem. Your answer should include all the conditions required for the theorem to hold. (4 marks) (b) Let y be the square contour with vertices at -3, -3i, 3 and 3i, described in the anti-clockwise direction. Evaluate に dz. You must check all of the conditions of any results that you use. (5 marks) (c) Evaluate L You must check all of the conditions of any results that you use. ཙ x sin(Tx) x²+2x+5 da. (11 marks)

3. (a) Lety: [a, b] C be a contour. Let L(y) denote the length of y. Give a formula for L(y). (1 mark) (b) Let UCC be open. Let f: U→C be continuous. Let y: [a,b] → U be a contour. Suppose there exists a finite real number M such that |f(z)| < M for all z in the image of y. Prove that < ||, f(z)dz| ≤ ML(y). (3 marks) (c) State and prove Liouville's theorem. You may use Cauchy's integral formula without proof. (d) Let R0. Let w € C. Let (10 marks) U = { z Є C : | z − w| < R} . Let f UC be a holomorphic function such that 0 < |ƒ(w)| < |f(z)| for all z Є U. Show, using the local maximum modulus principle, that f is constant. (6 marks)

Chapter 6 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

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 given expression 9 x 2 + 7 x y − 2 y 2 completely.

Solution Summary: The author explains how to factor the given expression 9x2+7xy-2y2.

Concept explainers

Videos

To factor: The given expression 9x2+7xy−2y2 completely.

Want to see the full answer?

Chapter 6 Solutions