Question

Please help this is my last thing to do!!!
A rectangle has sides measuring (3x + 5) units and (6x + 11) units. Part A: What is the expression that represents the area of the rectangle? Show your work
Part B: What are the degree and classification of the expression obtained in Part A?
Part C: How does Part A demonstrate the closure property for polynomials?

Answer 1

In the top right corner, that small box has an area of 3x*6x = 18x^2

Answer 2

* whoops I meant top left

Answer 3

okay

Answer 4

what's the area in the rest of the boxes?

Answer 5

i dont know

Answer 6

55

Answer 7

yes 55 is the area of the bottom right box

great :)


what about the area of the bottom left box?

Answer 8

aka what is 5 * 6x = ?

Answer 9

30x

Answer 10

perfect

and what about the area of the top right box?

Answer 11

18x

Answer 12

11 * 3x = ?

Answer 13

ohh 33x

Answer 14

awesome

so if we add up all of the pieces:
18x^2 + 33x + 30x + 55

Answer 15

can you simplify that?

Answer 16

ok im working it out

Answer 17

63x+379

Answer 18

no only the 33x and the 30x can combine

so it would be 18x^2 + 63x + 55 as the area of your rectangle

Answer 19

oohh okay

Answer 20

The degree of a polynomial is the highest power in that equation

Answer 21

what does that mean

Answer 22

x^5 is a "5th degree polynomial"
x^4 is a "4th degree polynomial"
x^3 is a "3rd degree polynomial"
etc

Answer 23

ooh okay im getting it

Answer 24

so what's the degree value of 18x^2 + 63x + 55 ?

Answer 25

2nd degree

Answer 26

perfect

then the possible classifications are:
x is a monomial
x + 3 is a binomial
x^2 + 3x + 4 is a trinomial

Answer 27

what's the classification of 18x^2 + 63x + 55 ?

Answer 28

what do you mean by classification

Answer 29

then the possible classifications are:
x is a monomial
x + 3 is a binomial
x^2 + 3x + 4 is a trinomial

Answer 30

would it be trinomial

Answer 31

yup!

Answer 32

so now you have your answer for part B
the degree and the classification

Answer 33

how would i do that thought

Answer 34

what?

Answer 35

\(\color{#0cbb34}{\text{Originally Posted by}}\) @trickesareforkids
2nd degree
\(\color{#0cbb34}{\text{End of Quote}}\)

\(\color{#0cbb34}{\text{Originally Posted by}}\) @trickesareforkids
would it be trinomial
\(\color{#0cbb34}{\text{End of Quote}}\)

"Part B: What are the degree and classification of the expression obtained in Part A?"

Answer 36

nevermind

Answer 37

Finally, "closure property of polynomials" is asking: If you multiply two polynomials, does to make another polynomial?

Answer 38

So answer this:

Is 3x+5 a polynomial? yes or no

Is 6x + 11 a polynomial? yes or no

Is 18x^2 + 63x + 55 a polynomial? yes or no


If you answer yes for all three, then "closer property of polynomials" works

Answer 39

1 yes 2 yes 3 yes

Answer 40

so i guess its closer property of polynomial

Answer 41

yup!

Answer 42

yay ok

Answer 43

is that all or are there more steps

Answer 44

that's it!

Answer 45

okay thank you so much

Answer 46

no problem