I understand, just check please? A restaurant has x floors. The number of tables on each floor is 4 less than the number of floors. The number of chairs with each table is 1 less than the number of tables on each floor. The expression below shows the total number of chairs in the restaurant: x(x - 4)(x - 5) Part A: What does x(x - 4) represent? (4 points) Part B: What type of polynomial is x(x - 4)(x - 5)? (3 points) Part C: What is the degree of the polynomial x(x - 4)? (3 points)

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I understand, just check please? A restaurant has x floors. The number of tables on each floor is 4 less than the number of floors. The number of chairs with each table is 1 less than the number of tables on each floor. The expression below shows the total number of chairs in the restaurant: x(x - 4)(x - 5) Part A: What does x(x - 4) represent? (4 points) Part B: What type of polynomial is x(x - 4)(x - 5)? (3 points) Part C: What is the degree of the polynomial x(x - 4)? (3 points)

Mathematics
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Part A: x(x - 4) represents the number of tables on all floors. Part B: THIS IS WHERE I'M CONFUSED
Should I simplify it, and then find what kind of polynomial, binomial, trinomial it is? If so, can you help me with that?
the highest power on x will tell you what type it is . if you expand it what will the highest power on x be?

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Which step if first to expand it? Do I multiply (x-4)(x-5) first?
(you don't actually have to expand it, if you can recognise the highest order term will be x * x * x)
yeah, the degree would be three
yes?
I think I understand now, thank you for your help. :)
yep, all the other terms will be quadratic, linear, or constant but the cubic term is the only one that matters here
were the options polynomial, binomial, trinomial etc? if so, it is slightly different
Yeah, third degree trinomial. I got it thanks.
you do have to expand out the factors to determine the number of terms
The last part is 2nd degree
yes C is 2nd degree, but B is not a trinomial, (it is a cubic)
Oh. Thanks!
there are more than three terms if you expand it out
?
ax^3 + bx^2 + cx + d
but maybe b c or d is zero?
to expand x(x - 4)(x - 5) yeah expand (x - 4)(x - 5), first
\[x^2 - 9x + 20\]
Then you multiply the whole thing by x and get \[x^3 - 9x^2 + 20x\]
yes?
yes good show,
so it was a trinomial after all
ok, good.
it's a trinomial because it has three terms and its a cubic (3rd order) because the highest power of x is three
yes. great!

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