Question

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)

Answer 1

Part A: x(x - 4) represents the number of tables on all floors.

Part B: THIS IS WHERE I'M CONFUSED

Answer 2

Should I simplify it, and then find what kind of polynomial, binomial, trinomial it is? If so, can you help me with that?

Answer 3

the highest power on x will tell you what type it is .

if you expand it what will the highest power on x be?

Answer 4

Which step if first to expand it? Do I multiply (x-4)(x-5) first?

Answer 5

(you don't actually have to expand it, if you can recognise the highest order term will be x * x * x)

Answer 6

yeah, the degree would be three

Answer 7

yes?

Answer 8

I think I understand now, thank you for your help. :)

Answer 9

yep, all the other terms will be quadratic, linear, or constant
but the cubic term is the only one that matters here

Answer 10

were the options polynomial, binomial, trinomial etc?

if so, it is slightly different

Answer 11

Yeah, third degree trinomial. I got it thanks.

Answer 12

you do have to expand out the factors to determine the number of terms

Answer 13

The last part is 2nd degree

Answer 14

yes C is 2nd degree, but B is not a trinomial, (it is a cubic)

Answer 15

Oh. Thanks!

Answer 16

there are more than three terms if you expand it out

Answer 17

?

Answer 18

ax^3 + bx^2 + cx + d

Answer 19

but maybe b c or d is zero?

Answer 20

to expand

x(x - 4)(x - 5)

yeah expand (x - 4)(x - 5), first

Answer 21

\[x^2 - 9x + 20\]

Answer 22

Then you multiply the whole thing by x and get \[x^3 - 9x^2 + 20x\]

Answer 23

yes?

Answer 24

yes good show,

Answer 25

so it was a trinomial after all

Answer 26

ok, good.

Answer 27

it's a trinomial because it has three terms

and its a cubic (3rd order) because the highest power of x is three

Answer 28

yes. great!