SOLUTION: Can someone please help me factor this problem completely? x^10y^3 - 4x^9y^2 - 21x^8y????? Here is what I have as my attempt, but am not sure I am even correct with what I have

Question 101511This question is from textbook Intermediate Algebra
: Can someone please help me factor this problem completely?
x^10y^3 - 4x^9y^2 - 21x^8y?????
Here is what I have as my attempt, but am not sure I am even correct with what I have..
Simplify:
x^10y^3 - 36xy^2 - 168xy
x^10y^3 - 72xy - 168xy
Combine like terms:
72xy + 168xy = 240xy
240xy* x^10*y^3=?
This problem was given to me by my college Professor, but it is not from our textbook. Thanks. Below are additional directions from Professor:
**Make sure to superscript all exponents. If you believe that a polynomial is not factorable, label it as prime. Show all stages of factoring separately (i.e., show the result of factoring out a GCF before taking the resulting polynomial and factoring it again).**
This question is from textbook Intermediate Algebra

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.

.
First look at the numbers that multiply each of the terms to see if there is are common
factors. The first term is multiplied by 1 (understood), the second term by -4, and the
third term by -21. These three numbers have no common factors, so we don't change them.
.
Next look at the x part of each of the terms. The first term contains , the second
term , and the third term . is common to each term because
and . So we can pull an from each term and
we get:

.
Next notice that you have a "y" common to all terms. So pull a y out as a multiplier and
you have:
.

.
Notice that we can multiply out and the result should be
the original given expression. This is just a "check".
.
So we are down to . We now need to see if we can factor the
Yes we can. It might be a little easier to see if we wrote
in an equivalent form of to change the expression to:
.
and we might see it a little more clearly if we let xy = A to get:
.

.
We can try to factor this into (A + ___)*(A + ___). The underscores have to be two numbers
that are factors of -21. These numbers could be 21 and 1 or 7 and 3. With their appropriate signs
they must sum to -4. -7 and + 3 do that. If they are multiplied they give -21 and if they are
added they give -4 which is the multiplier of the center term that contains just A.
.
So we can write that factors to . But also recall
that we said A was equal to xy. So now we can substitute xy into the two factors and get:
.

.
And so we can say that factors to and we can
carry this result back into this equation that we got earlier:
.

.
In this equation, replace with and the result is:
.

.
and that's the answer to your problem.
.
I know this is confusing, but I hope that you can see your way through it. If you can
understand all the maneuvering in this you will have made a lot of progress.
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