SOLUTION: Factor if possible 3(x-2y)^2 + 6(x-2y) - 45 **The answer has to be one of these choices 3(x+2y+5)(x-2y-3) , 3(x-2y-5)(x-2y+3), 3(x+2y-5)(x-2y+3) , 3(x-2y+5)(x-2y-3)

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Let


So the expression becomes




Start with the given expression


Factor out the GCF


Now let's focus on the inner expression




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Looking at we can see that the first term is and the last term is where the coefficients are 1 and -15 respectively.

Now multiply the first coefficient 1 and the last coefficient -15 to get -15. Now what two numbers multiply to -15 and add to the middle coefficient 2? Let's list all of the factors of -15:



Factors of -15:
1,3,5,15

-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -15
(1)*(-15)
(3)*(-5)
(-1)*(15)
(-3)*(5)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

First Number	Second Number	Sum
1	-15	1+(-15)=-14
3	-5	3+(-5)=-2
-1	15	-1+15=14
-3	5	-3+5=2

From this list we can see that -3 and 5 add up to 2 and multiply to -15


Now looking at the expression , replace with (notice adds up to . So it is equivalent to )




Now let's factor by grouping:


Group like terms


Factor out the GCF of out of the first group. Factor out the GCF of out of the second group


Since we have a common term of , we can combine like terms

So factors to


So this also means that factors to (since is equivalent to )



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So our expression goes from and factors further to




Remember we let , so let's replace z with x-2y

Plug in




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Answer:

So factors to


So the answer is D)