Question

http://www.usatestprep.com/modules/gallery/files/27/2729/2729.png

Which expression represents the volume of the rectangular prism shown?
A)
3x4 + 11
B)
x2 + 2x + 11
C)
x4 + 11x3 + 24x2
D)
x3 + 3x2 + x + 8

Answer 1

Volume of a rectangular prism is L * W * H.

So we have:

\((x+3)(x+8)(x^2)\)

Can you multiply those together?

Answer 2

First let's multiply:

\((x+3)(x+8)\)

x * x =?
x * 8 = ?

3 * x = ?
3 * 8 = ?

Answer 3

u cant do x*8 or 3*x

Answer 4

Yes, you can..they become 8x and 3x.

What about x * x?

Answer 5

And 3 * 8?

Answer 6

2x?

Answer 7

are you just combinding them?

Answer 8

No, actually it becomes \(x^2\)

Remember, exponents multiply the base by itself.

2 * 2 is the same thing as \(2^2\)

Answer 9

Yes, that's what we do with x * 8 and 3 * x

What about 3 * 8?

Answer 10

24

Answer 11

Yes, so we have:

\(x^2 + 8x + 3x + 24\)

Now we add 8x + 3x, which is the same thing as 8 + 3, but we put the variable next to it. So that becomes 11x

\(x^2 + 11x + 24\)

Now we multiply this by \(x^2\)

\((x^2 + 11x + 24)(x^2)\)

x^2 * x^2
11x * x^2
24 * x^2

Answer 12

Remember, we add the exponents if we have the same base:

\(x^2 \cdot x^2 \rightarrow x^{2 + 2}\)

Answer 13

x^4

Answer 14

Yep, what's 11x * x^2?

Answer 15

Actually, we already have our answer..only one option has \(x^4\) in it..

Answer 16

y did you multiply x^2

Answer 17

Why did I multiply x^2 * x^2?

Answer 18

Is that what you're asking?

Answer 19

no y did you multiply by X^2

Answer 20

Because it told us to..

We had to multiply:

\((x + 3)(x + 8)(x^2)\)

We multiplied \((x + 3)(x + 8)\) first..and we got \(x^2 + 11x + 24\), now we had to multiply:

\((x^2 + 11x + 24)(x^2)

Answer 21

so the answer is c right?

Answer 22

Yep, you got it.

Answer 23

thanks