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6.8 Summary of key concepts

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This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Factoring is an essential skill for success in algebra and higher level mathematics courses. Therefore, we have taken great care in developing the student's understanding of the factorization process. The technique is consistently illustrated by displaying an empty set of parentheses and describing the thought process used to discover the terms that are to be placed inside the parentheses.The factoring scheme for special products is presented with both verbal and symbolic descriptions, since not all students can interpret symbolic descriptions alone. Two techniques, the standard "trial and error" method, and the "collect and discard" method (a method similar to the "ac" method), are presented for factoring trinomials with leading coefficients different from 1. This module provides a summary of the key concepts in the chapter "Factoring Polynomials".

Summary of key concepts

Factoring ( [link] )

Factoring is the process of determining the factors of some product. Factoring is the reverse of multiplication.

Greatest common factor ( [link] )

The greatest common factor of a polynomial is the factor that is common to every term of the polynomial and also is such that
  1. The numerical coefficient is the largest number common to each term.
  2. The variables possess the largest exponents that are common to all the variables.

Factoring a monomial from a polynomial ( [link] )

If A is the greatest common factor of A x A y , then
A x A y A ( x y )

Factoring by grouping ( [link] )

We are alerted to the idea of factoring by grouping when the polynomial we are considering
  1. Has no factor common to all terms.
  2. Has an even number of terms.
A x + A y ⎵ A   is   common + B x + B y ⎵ B   is   common = A ( x + y ) + B ( x + y ) ⎵ x + y   is   common = ( x + y ) ( A + B ) A x plus A y plus B x plus B y equals the product of A and x plus y; plus the product of B and X plus y. The first two terms of the polynomial on the left side have A in common, and the last two terms have B in common. Two terms on the right side have x plus y in common.

Special products ( [link] )

a 2 − b 2 = ( a + b ) ( a − b ) a 2 + 2 a b + b 2 = ( a + b ) 2 a 2 − 2 a b + b 2 = ( a − b ) 2

Fundamental rule of factoring ( [link] )

  1. Factor out all common monomials first.
  2. Factor completely.

Factoring trinomials ( [link] , [link] )

One method of factoring a trinomial is to list all the factor pairs of both of the first and last terms and then choose the combination that when multiplied and then added produces the middle term.

Questions & Answers

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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