#1**+1 **

Best Answer

There are 2 combinations of x^2, x, and 1 that will have x^3.

x^2, x, 1, 1 and x, x, x, 1

x^2, x, 1, 1 = 4*3*2/2 = 12 ways to organize

x, x, x, 1 = 4*3*2/3/2 = 4 ways to organize

4 + 12 = 16

=^._.^=

catmg Jun 18, 2021

#2**+1 **

That's an interesting method, catmg.....I haven't seen that before.......where did you find this (or learn it ??? )

CPhill
Jun 18, 2021

#3**+1 **

You're choosing one term from each thing you're multiplying by.

It's similar to the idea of the binomial theorum.

For example...

(x+1)(x+1) or (x+1)^2

If you were to fully expand it.

x*x + 1*x + x*1 + 1*1, in each pair, you're choosing 1 term from each "x+1".

There is only 1 way to get an x^2, choosing x for the first pair, and then choosing it again in the second pair.

There are 2 ways to get an x, choosing x first pair then a 1 second pair, or 1 first pair and x second pair.

I hope that made sense. :))

=^._.^=

catmg
Jun 18, 2021