Part A: The area of a square is (4x^2 - 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work.
Part B: The area of a rectangle is (16x^2 - 9y^2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show
your work.

Area = side²

If Area = 4x² + 12x + 9, then the side is the √(4x² + 12x + 9)

Let’s factor 4x² + 12x + 9

What two numbers multiply to be 36 (which came from 4 * 9) add up to be 12?

6 and 6 are the two numbers, because 6 * 6 = 36, and 6 + 6 = 12.

We can break 4x² + 12x + 9 into (4x² + 6x) + (6x + 9)

Factor 4x² + 6x, the greatest common factor is 2x, so the 2x goes on the outside, leaving us with 2x + 3 on the inside, so that gives us 2x * (2x + 3).

Factor 6x + 9, the greatest common factor is 3, so the 3 goes on the outside, leaving us with 2x + 3 on the inside, that gives us 3 * (2x + 3).

Now we have the 4x² + 12x + 9 written as 2x (2x + 3) + 3 (2x + 3). Since we now have a common factor, 2x + 3, we can combine them by adding 2x (2x + 3) + 3 (2x + 3) as like terms, so we now have (2x + 3) * (2x + 3).

We can simplify (2x + 3)(2x + 3) into (2x + 3)².

There. The simplest factored form of 4x² + 12x + 9 is (2x + 3)²

Ok, the Area = (2x + 3)²

Let’s solve for the side

(2x + 3)² = side²

square root both sides and take the positive root

side = √(2x + 3)²

side = 2x + 3

The side length is: 2x + 3 units

I hope you get a good grade lol :)

Step-by-step explanation:

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value