SOLUTION: Factoring with two variables. Factor each polynomial: h^2-9hs + 9s^2

Question 211173: Factoring with two variables.
Factor each polynomial: h^2-9hs + 9s^2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last coefficient is .

Now multiply the first coefficient by the last coefficient to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,3,9
-1,-3,-9

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*9 = 9
3*3 = 9
(-1)*(-9) = 9
(-3)*(-3) = 9

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	9	1+9=10
3	3	3+3=6
-1	-9	-1+(-9)=-10
-3	-3	-3+(-3)=-6

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

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