Suppose 3s represents an even integer. What polynomial represents the product of 3s, the even integer that comes just before 3s, and the even integer that comes just after 3s?

A) 27s^3 + 12s
B) 27s^3 - 3s
C) 27s^3 - 12s
D) 3s^3 - 12s

Question

Suppose 3s represents an even integer. What polynomial represents the product of 3s, the even integer that comes just before 3s, and the even integer that comes just after 3s?

A) 27s^3 + 12s
B) 27s^3 - 3s
C) 27s^3 - 12s
D) 3s^3 - 12s

directrix · Answer

Even integers differ by two. If 3s is even, the even just below 3s is (3s -2) and the even just above 3s would be (3s+2).

Now, just multiply (3s -2) * (3s) * (3s +2) and see what you get. Start with (3s) * (3s -2) and post what that product is.

anonymous · Answer

i dont understand what the s is for and im not really sure what your asking me to do

anonymous · Answer

im also not sure how to put this in my calculator

directrix · Answer

s is any integer. Is s = 3, the 2s = 6.
If s = 4, the 2s = 8.
The idea is to realize that an even number times an odd = even.

Those terms won't go in my calculator except for the calculator on my neck, seriously.

If 3s is even, then 3s +2 is even, and the same for 3s -2. Evens differ by a multiple of 2.

directrix · Answer

(3s) (3s -2) ==> the product of these. Just use the distributive property.

anonymous · Answer

9s-6s?

directrix · Answer

(9s^s -6s)--? 3s times 3s = 3 times 3 times s times s = 9s^2

Multiply these: (9s^s -6s) (3s + 2) and you'll be finished. The first term is NOT 27 s^2.

Post here and I'll check.

anonymous · Answer

idk how to this

anonymous · Answer

is it 27^3 - 3s

directrix · Answer

Yes, you do. 
It's the (a+b) (c + d) pattern.

(9s^s -6s) (3s + 2)

Do these and post:

9x^2 times 3s -->
9s^2 times 2 --->
(-6s) times 3s --->
and
(-6s) times 2 ---->

Write these 4 results here.

anonymous · Answer

i still dont know what im doing idk what the s is for

anonymous · Answer

idk where u got x from too

directrix · Answer

I don't see any xs so I don't know about them.
Forget about s. It's a variable.
Your task is to multiply the terms I wrote for you.


9x^2 times 3s -->
9s^2 times 2 --->
(-6s) times 3s --->
and
(-6s) times 2 ---->

I'll be back to check.

anonymous · Answer

im confused on of your anwers you and and x that isnt supposed to be there and i have no idea how to do your work

anonymous · Answer

im to the point where im about to just guess because this is all really confusing

directrix · Answer

What confuses me is what you will REFUSE to multiply these:

9x^2 times 3s -->
9s^2 times 2 --->
(-6s) times 3s --->
and
(-6s) times 2 ---->
Don't worry if what you write is incorrrect. That is not an issue.  So, just do it, please.

anonymous · Answer

im not rufussing i dont know how to multiply the numbers you gave me

directrix · Answer

How did you know how to do this earlier:      (3s) (3s -2) =     9s-6s?
Of course, it was 9 s^2 - 6s but you were close. So, you know how to multiply. Just do it on those others.

anonymous · Answer

81
243
162
-18
-12 this is what i got idk if its write

directrix · Answer

Hey, I see what you mean about the x.

(3s -2) * (3s) * (3s +2) =
(3s)(3s - 2) = 9s^2 - 6s

(9s^2 -6s) ((3s + 2) =
27s^3 + 18s^2 + ? + ??

Your task is now the following:

(-6s)(3s) =
and
(-6s)(2) =

You do those two and we may be finished. :)

anonymous · Answer

-18 
-12

directrix · Answer

Why is it that you disregard the variables? In Algebra, there will always be variables.

anonymous · Answer

-18s
-12s

directrix · Answer

(3s -2) * (3s) * (3s +2) =
(3s)(3s - 2) = 9s^2 - 6s

(9s^2 -6s) ((3s + 2) =
27s^3 + 18s^2 + ? + ??

(-6s)(3s) = -18s^2
and
(-6s)(2) = -12s
---------------------
(3s -2) * (3s) * (3s +2) = 27s^3 - 12s---> Answer

anonymous · Answer

thank you

directrix · Answer

Glad to help. Learn to multiply those variables.