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- Factoring polynomials
- Summary of key concepts
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
- The numerical coefficient is the largest number common to each term.
- The variables possess the largest exponents that are common to all the variables.
Factoring a monomial from a polynomial (
[link] )
If
is the greatest common factor of
, then
Factoring by grouping (
[link] )
We are alerted to the idea of
factoring by grouping when the polynomial we are considering
- Has no factor common to all terms.
- Has an even number of terms.
Special products (
[link] )
Fundamental rule of factoring (
[link] )
- Factor out all common monomials first.
- 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
(Pcos∅+qsin∅)/(pcos∅-psin∅)
how to answer the activity
how to solve the activity
Chabelita
solve for X,,4^X-6(2^)-16=0
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t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
If
, ,
are the roots of the equation
3 2 0,
x px qx r
Find the value of
1
.
Parts of a pole were painted red, blue and yellow. 3/5 of the pole was red and 7/8 was painted blue. What part was painted yellow?
Parts of the pole was painted red, blue and yellow. 3 /5 of the pole was red and 7 /8 was painted blue. What part was painted yellow?
Patrick
how I can simplify algebraic expressions
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?
lairenea's age is 23yrs
ACKA
Laurene is 46 yrs and Mae is 23 is
Solomon
age does not matter
christopher
solve for X, 4^x-6(2*)-16=0
Alieu
prove`x^3-3x-2cosA=0
(-π<A<=π
create a lesson plan about this lesson
Excusme but what are you wrot?
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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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