SOLUTION: We just started factoring polynomials and I don't understand how you can tell if a problem when you first look at it,doesn't have a greater common factor.For example my teacher had

Question 108826: We just started factoring polynomials and I don't understand how you can tell if a problem when you first look at it,doesn't have a greater common factor.For example my teacher had this one:21x-7 and another one was:x^9y^6-x^7y^5+x^4y^4+x^3y^3
This so confusing to me,if you could help I would really appreciate it.Thank you in advance JH
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
When you look at each expression, are there common factors??

In that example, the number 7 was commmon.
In the next example, it's powers of x and y.
Remember your exponent rules.

Here's the equation.
What's the lowest power of x common to each expression??

Similarly, what's the lowest power of y common to each expression??

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
how you can tell if a problem when you first look at it,doesn't have a greater common factor.For example my teacher had this one:
21x-7
You have to see that 21 is the product of 3 and 7
You have to see that you have two terms: 21x and -7
Then you might see that "7" is a factor common to both terms
So, you "factor out" the 7 by dividing each term by 7 to get:
7(3x-1)
====================
x^9y^6 - x^7y^5 + x^4y^4 + x^3y^3
Checking the four terms you have to see there is a common
factor of x^3 in each term and a common factor of y^3 in
each term.
Divide each terms by x^3y^3 to get:
x^3y^3 (x^6x^3 -x^4y^3 +xy + 1)
================
Hope that helps.
Cheers,
Stan H.

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