SOLUTION: I have tried this using our book and I just don't udestand the process. My teacher is of no help, she just keeps pointing me to our book. Factor each polynomial completely. a

Question 101585: I have tried this using our book and I just don't udestand the process. My teacher is of no help, she just keeps pointing me to our book.
Factor each polynomial completely.
a) x^3y+2x^2y^2+xy^3
b) -4w^3-16w^2+20w
c) 3x^2 � 17x + 10
Thank you so much for any help you can provide me with. :)
d) -36a^2b + 21ab^2 � 3b^3
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
I have tried this using our book and I just don't udestand the process. My teacher is of no help, she just keeps pointing me to our book.
Factor each polynomial completely.
a) x^3y+2x^2y^2+xy^3
b) -4w^3-16w^2+20w
c) 3x^2 � 17x + 10
Thank you so much for any help you can provide me with. :)
d) -36a^2b + 21ab^2 � 3b^3

a) by inspection, we see that we can take an out of each term so lets do that:
Again, by inspection, we see that is a perfect square but we can also do the following:
and we can re-write this as follows:
now we can factor out an and we get:
or
------------------ans

b) by inspection, we see that we can take a out of each term so lets do that:
Now we observe that is a quadratic in standard form. When we have a quadratic in standard form and the A coefficient is 1 then the B coefficient is the sum of the factors of the C coefficent. What are the factors of the C coefficient?? They can only be or . By inspection we see that +5 and -1=+4. So now we know that: =. Now putting it all back together, we have:
---------------------ans
c) Here are the possibilities:
By inspection, we see that if this quadratic can be factored, then the factors must be of the form (a-b)(c-d) or (c-b)(a-d). Why??? Because the last term is positive and the middle term is negative. So here are the possibilities:
1.
2.
3.
4.
Expanding each of the above using the FOIL crutch (First, Inner, Outer, Last) we get:
1.-----------------NO!!! inner term is -13x
2.------------------NO!!! inner term is -31x
3.-------------------NO!!!! inner term is -7x
4.----------------BINGO!!!!!!!
-----------------------ans
d) By inspection, we see that we can take a -3b out of each term:
Now use the approach that was used in (c) above and find the factors for . I bet you can do it!!!!!

Hope this helps---ptaylor

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