Question

Minnie has a piece of cardboard with length (3x2 − 2x + 1) inches and width (2x2 + 3x − 4) inches. Which statement best explains why the area of the cardboard demonstrates the closure property?

Answer 1

Minnie has a piece of cardboard with length (3x2 − 2x + 1) inches and width (2x2 + 3x − 4) inches. Which statement best explains why the area of the cardboard demonstrates the closure property?

It is equal to (6x4 + 9x3 − 12x2 + 8x − 4) square inches, which is also a polynomial like the length and width.
It is equal to (6x4 + 5x3 − 16x2 + 11x − 4) square inches, which is also a polynomial like the length and width.
The length multiplied by the width is equal to the width multiplied by the length.
The length multiplied by the width has the same degree as the width multiplied by the length.

Answer 2

@Michele_Laino

Answer 3

@uri @Preetha

Answer 4

hint:
area of a rectangle is given by the subsequent formula:
\[{\text{area = base }} \times {\text{ height}}\]

Answer 5

so we can write:
\[\Large \begin{gathered}
{\text{area = base }} \times {\text{ height = }} \hfill \\
= \left( {3{x^2} - 2x + 1} \right) \times \left( {2{x^2} + 3x - 4} \right) = ...? \hfill \\
\end{gathered} \]

Answer 6

so its gonna be 6x^4-6x^2-4 correct?

Answer 7

I got a different result

Answer 8

uhmm

Answer 9

hint:
\[\Large \begin{gathered}
\left( {3{x^2} - 2x + 1} \right) \times \left( {2{x^2} + 3x - 4} \right) = \hfill \\
= 6{x^4} + 9{x^3} - 12{x^2} - 4{x^3} - 6{x^2} - 4 = ...? \hfill \\
\end{gathered} \]

Answer 10

how did you get that

Answer 11

I have applied the distributive peroperty of multiplication over addition

Answer 12

ohhh

Answer 13

so now what do i do?

Answer 14

more explanation:
\[\large \begin{gathered}
\left( {3{x^2} - 2x + 1} \right) \times \left( {2{x^2} + 3x - 4} \right) = \hfill \\
= 3{x^2} \times \left( {2{x^2} + 3x - 4} \right) - 2x \times \left( {2{x^2} + 3x - 4} \right) + 1 \times \left( {2{x^2} + 3x - 4} \right) = ...? \hfill \\
\end{gathered} \]

Answer 15

\[\begin{gathered}
\left( {3{x^2} - 2x + 1} \right) \times \left( {2{x^2} + 3x - 4} \right) = \hfill \\
= 3{x^2} \times \left( {2{x^2} + 3x - 4} \right) - 2x \times \left( {2{x^2} + 3x - 4} \right) + 1 \times \left( {2{x^2} + 3x - 4} \right) = ...? \hfill \\
\end{gathered} \]

Answer 16

this is gonna be really drawn out

Answer 17

6x^4+9x3-12x^2-4x^3-6x^2+8x+2x^2+3x-4?

Answer 18

yes! you are right! sorry I have meade an error in my previous result

Answer 19

now you have to simplify similar terms, what do you get?

Answer 20

ohh crap uhmm

Answer 21

can you help me on this i dont really know

Answer 22

oops.. I have made*

Answer 23

grouping similar term, we can write:
\[\Large 6{x^4} + {x^3}\left( {9 - 4} \right) + {x^2}\left( { - 12 - 6 + 2} \right) + x\left( {8 + 3} \right) - 4 = ...?\]

Answer 24

\[\large 6{x^4} + {x^3}\left( {9 - 4} \right) + {x^2}\left( { - 12 - 6 + 2} \right) + x\left( {8 + 3} \right) - 4 = ...?\]

Answer 25

uhmm idk

Answer 26

what is 9-4=...?

Answer 27

5

Answer 28

ok!
and
-12-6+2=...?
8+3=...?

Answer 29

-16 and 11

Answer 30

that's right!
So, what is the resulting polynomial?

Answer 31

what you mean

Answer 32

you have to substitute the coefficients which you have fount into this expression:
\[6{x^4} + {x^3}\left( {9 - 4} \right) + {x^2}\left( { - 12 - 6 + 2} \right) + x\left( {8 + 3} \right) - 4 = ...?\]

Answer 33

found*

Answer 34

so im still confused? what did we just do with the addition and subtraction?

Answer 35

is the answer C?

Answer 36

the resulting polinomial is:
\[\begin{gathered}
\left( {3{x^2} - 2x + 1} \right) \times \left( {2{x^2} + 3x - 4} \right) = \hfill \\
\hfill \\
= 3{x^2} \times \left( {2{x^2} + 3x - 4} \right) - 2x \times \left( {2{x^2} + 3x - 4} \right) + 1 \times \left( {2{x^2} + 3x - 4} \right) = \hfill \\
\hfill \\
= 6{x^4} + {x^3}\left( {9 - 4} \right) + {x^2}\left( { - 12 - 6 + 2} \right) + x\left( {8 + 3} \right) - 4 = \hfill \\
\hfill \\
= 6{x^4} + 5{x^3} - 16{x^2} + 11x - 4 \hfill \\
\end{gathered} \]

Answer 37

dang sorry i was confused but thank you so much you were a huge help!!! xD

Answer 38

it is the second option

Answer 39

please wait, I think it is the fourth option, because we got a fourth-degree polynomial, whereas the length and the width are two second-degree polynomials