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

Answer:

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

Part b) $3x+6$

Step-by-step 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].

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:

$\frac{6x^2+12x}{2x}$

$\frac{6x^2}{2x}+\frac{12x}{2x}$

$3x+6$

Answer 2

Answer:

A) 2x(2x - 5)

B) -(3x + 6)

Step-by-step 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