How can I factor these polynomials?

[cjackson]

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.

 

[Simon Bridge]

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?

 

[Mentallic]

$$a^3=a\times a^2$$
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 $2^1\times 3^1=2\times 3 = 6$.

 

[cjackson]

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.

 

[cjackson]

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

 

[Mark44]

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.

Here are some more examples from the book.

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

x^2+5x+6

3y^2+8y+4