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 3 Q 2 + Q − 30 as follows. It is observed that, the coefficients are a = 3 , b = 1 and c = − 30 . Step 1: Find the value of a c . Obtain the value of a c as, a c = 3 ( − 30 ) = − 90 Thus, the value of a c is –90. Step 2: Find the two number, m and n, whose product is a c = − 90 and whose sum is b = 1 . Obtain the list of integer factors of –90 such that product is –90 and sum is 1 as shown below in Table 1. Integers whose product is –90 1 , − 90 − 10 , 9 10 , − 9 − 1 , 90 Sum –89 –1 1 89 Table 1 From Table 1, it is observed that the numbers whose product is –90 and sum is 1 are − 9 and 10 . Let, the integers take the variables m = − 9 and n = 10

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For Basic Technical Mathematics With Calculus

11th Edition

ISBN: 9780135902912

Author: Allyn J. Washington

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 6.2, Problem 59E

To determine

To factor: The expression 3Q2+Q−30 completely.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.2, Problem 58E

Chapter 6.2, Problem 60E

Students have asked these similar questions

This is advanced mathematics question that need detailed solutions

Question: Let F be a field. Prove that F contains a unique smallest subfield, called the prime subfield, which is isomorphic to either Q or Zp for some prime p. Instructions: • Begin by identifying the identity element 1 € F. • Use the closure under addition and inverses to build a subring. • • • Show that either the map ZF or Q →F is an embedding. Prove minimality and uniqueness. Discuss the characteristic of a field and link it to the structure of the prime subfield.

Topic: Group Theory | Abstract Algebra Question: Let G be a finite group of order 45. Prove that G has a normal subgroup of order 5 or order 9, and describe the number of Sylow subgroups for each. Instructions: • Use Sylow's Theorems (existence, conjugacy, and counting). • List divisors of 45 and compute possibilities for n for p = 3 and p = 5. Show that if n = 1, the subgroup is normal. Conclude about group structure using your analysis.

Chapter 6 Solutions

Mylab Math With Pearson Etext -- 18 Week Standalone Access Card -- For 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 3 Q 2 + Q − 30 completely.

Videos

To factor: The expression 3Q2+Q−30 completely.

Want to see the full answer?

Chapter 6 Solutions