Question

40 POINTS!

Please look at the two small pictures below. Here are the questions.
7. a) Write a multiplication statement to represent the algebra tiles. (picture #1)

b) If the tiles below are divided by 2x, what is the quotient?

Answer 1

A) 2x(2x - 5)

B) -(3x + 6)

Explanation:

Each empty square represents: x²

Each filled rectangle represents: -x

Area is 4x² - 10x

There are two rows:

Each row is: 2x² - 5x = x(2x - 5)

Statement:

2x(2x - 5)

In b, there are 6 tiles of -x², and 12 tiles of -x, which makes it:

-6x² - 12x

-(6x² + 12x)

-(6x² + 12x)/2x

-[(6x²/2x) + (12x/2x)0

-(3x + 6)

-3x - 6

Answer 2

Part a)
`-2x(2x-5)`

Part b)
`3x+6`

Explanation:

Part a)

I first determined what each piece in the rectangular array meant.

Then I wanted to figure out the height and the base length.

I know
`-x(x)=-x^2` so that is why I put those purple
`x`'s on top and purple
`-x`'s down alongside for the
`-x^2` pieces. To get
`x` when I already had
`-x`, I needed to multiply by -1 which is why there is a -1 along the top where those
`x` pieces are.

So in the first question down the side of the box, we have
`-x+-x=-2x/tex]. </p><p>Along the the top we have [tex]x+x-1-1-1-1-1=2x-5`.

To find the area of the rectangle, you multiply height by base.

`-2x(2x-5)`.

Part b)We have six
`x^2`'s and twelve
`x`'s. So that means the polynomial represented here is
`6x^2+12x`.

What happens if we divide that by
`2x`.

Let's see:

`(6x^2+12x)/(2x)`

`(6x^2)/(2x)+(12x)/(2x)`

`3x+6`