How can I factor these polynomials?

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    Polynomials
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Discussion Overview

The discussion revolves around the process of factoring polynomials, specifically focusing on finding the greatest common factor (GCF) and the factorization of various types of polynomials, including monomials, binomials, trinomials, and quadratic equations. Participants share examples and seek clarification on the methods involved.

Discussion Character

  • Homework-related, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asks for help with factoring and provides an example involving polynomials.
  • Another participant points out that certain variables (d and e) are common factors in the provided example.
  • A participant explains the concept of the greatest common factor using variables and numerical examples, emphasizing the importance of prime factorization.
  • There is a reiteration of the common factors in the original example, confirming its source from the book.
  • A participant requests clarification on how to factor different types of polynomials and provides additional examples from the book.
  • One participant notes that the general factorization of polynomials is complex and suggests that the book likely contains worked examples, indicating a limitation in addressing broad topics in the forum.

Areas of Agreement / Disagreement

Participants generally agree on the importance of identifying common factors and the process of finding the GCF, but there is no consensus on how to approach the broader topic of polynomial factorization, as some participants express that it is too complex for the forum format.

Contextual Notes

The discussion highlights limitations in addressing comprehensive factorization techniques and suggests reliance on the book for detailed examples and explanations.

cjackson
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I'm in desperate need of help with factoring. Basically, how do you do it?

Below is an example of what I'm up against.

54c^2d^5e^3; 81d^3e^2

It wants me to find the greatest common factor.

http://www.rempub.com/80-activities-to-make-basic-algebra-easier

That is the book I'm working out of.
 
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Notice that d and e are factors in common?
BTW: just checking - is that an actual example from the book or one you made up?
 
a^3=a\times a^2
So if you wanted to find the greatest common factor of a^2; a^3 then it would be a^2. Basically, if you have any a^n for n greater than 2, then the common factor will always be the one with the smallest power index, in this case 2.

m^3n^5; n^7m^2
In this case, the smallest index of the m's is 2, and the smallest of the n's is 5, hence the greatest common factor is m^2n^5.

For numbers, you need to break them up into their prime factors. For example,
12=4\times 3 = 2^2\times 3
and
90 = 9\times 10 = 3^2\times 2\times 5

This is the same problem as earlier with the variables, but now we just have numbers where variables would've otherwise been. It's the exact same procedure though, as long as you break the number into its prime factors.
So to find the great common factor of 12 and 90, we notice that the highest power of the 2's is 1 (hence just 2^1=2), the highest power of the 3's is 1, and 5 is only present in one of the numbers so no 5 common factor. Hence the answer is 2^1\times 3^1=2\times 3 = 6.
 
Simon Bridge said:
Notice that d and e are factors in common?
BTW: just checking - is that an actual example from the book or one you made up?
It's straight from the book.
 
How do I factor monomials, binomials, trinomials and quadratic equations?

Here are some more examples from the book.

24x^3y^2-20x^2y^2+16xy^2

x^2+5x+6

3y^2+8y+4
 
cjackson said:
How do I factor monomials, binomials, trinomials and quadratic equations?
General factorization of polynomials is too involved for us to attempt to answer it here in an online forum. Your book must show worked examples of each type. If you have a question about a particular step in a single factorization, we can help you with that, but our role here is not to teach you a broad topic in algebra or other area of mathematics.

Thread closed.
cjackson said:
Here are some more examples from the book.

24x^3y^2-20x^2y^2+16xy^2

x^2+5x+6

3y^2+8y+4
 

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