Answer:
Of the 600 elephants that he observes in random places in the reserve, he counts 
elephants with broken tusks.
Step-by-step explanation:
Let x denotes number of elephants having broken tusks out of 600 elephants.
Of the 30 elephants that he observes in random places in the reserve, he counts 8 elephants with broken tusks.
So,
Of the 1 elephants that he observes in random places in the reserve, he counts 
elephants with broken tusks.
Therefore,
Of the 600 elephants that he observes in random places in the reserve, he counts elephants with broken tusks.
So essentially, we have a choice of :
2 reception halls
3 DJs
2 catering companies.
In order to find the number of arrangements, you need to multiply those : 2*3*2=12- So they have 12 arrangements.
why?
Imagine those 3 Djs- they are three arrangements.
Now, they can play in one or the other hall -so in total it's 3 Djs in one hall and 3 in the other -that's 6.
And all of those 6 possibilities can be catered by one or the other company- making the possibilities twice as many, so it's 12 in total!
Problem 1 is fully factored as each term is a binomial raised to some exponent. If the exponent isn't showing up, it's because it is 1. Recall that x^1 = x.
Problem 2 can be factored further because x^2-8x+16 factors to (x-4)(x-4) or (x-4)^2. To get this factorization, you find two numbers that multiply to 16 and add to -8. Those two numbers are -4 and -4 which is where the (x-4)(x-4) comes from. Overall, the entire thing factors to (x-4)^2*(x+3)*(x-2)
Problem 3 is a similar story. We can factor x^2-1 into (x-1)(x+1). I used the difference of squares rule here. Or you can think of x^2-1 as x^2+0x-1, then find two numbers that multiply to -1 and add to 0. Those two numbers are +1 and -1 which leads to (x+1)(x-1). So the full factorization is (x-1)(x+1)(x+1)(x-4) which is the same as (x-1)(x+1)^2(x-4)
