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

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