Question

Consider the rectangle below.
I
=
The area of a rectangle is the product of the length and the width, or
Questions:
1. What is the area of the rectangle?
2. Is the area of the rectangle a polynomial?
3. What is the relationship between the area of the rectangle and its sides?
4. What can you say about the width of the rectangle comparing it to the area?
5. What do you call the process of rewriting the polynomial as a product of
polynomial factors?​

Answer 1

Answer:

Answer 1 -To find the area of a rectangle, multiply its height by its width. For a square you only need to find the length of one of the sides (as each side is the same length) and then multiply this by itself to find the area.

answer 2-The area of a rectangle is expressed by the polynomial A(x) = 6x^2+17x+12.

answer 3-Also, using this approach, we find that the area of a rectangle is always the product of its two sides. Here, the length of AB is 8 inches and the length of BC is 6 inches. The area of ABCD is the product of 6 and 8, which is equal to 48.

answer 4-Thus, the width is constant, any value of length and area, the width still two (2) since it is constant. Since width is 2, and the formula for area is length times width, therefore the value of area is doubled to its length. The width indicates that any value of length, the area is only twice of its length.

answer-5-However, sometimes it will be more useful to write a polynomial as a product of other polynomials with smaller degree, for example to study its zeros. The process of rewriting a polynomial as a product is called factoring

Answer 2

Given: A rectangle.

To find:

1. The area of the rectangle.

2. If the area of the rectangle is a polynomial.

3. The relationship between the area of the rectangle and its sides.

4. The width of the rectangle comparing it to the area.

5. The process of rewriting the polynomial as a product of polynomial factors.

Solution:

Let the length and the width of the rectangle be l and w, respectively.

1.

The area of a rectangle can be calculated by using the following formula.

$Area = l * w$

2.

Yes, the area of a rectangle is a polynomial as it is the product of its length and width.

3.

The relationship between the area of a rectangle and its sides is that the area of a rectangle is the product of its two adjacent sides.

4.

On rearranging the formula of the area of a triangle, the width can be written as

$b = \frac{A}{w}$

5.

The process of rewriting the polynomial as a product of polynomial factors is called factorization.

Therefore,

1. The area of the rectangle is l*b.

2. The area of the rectangle is a polynomial

3. The relationship between the area of the rectangle and its sides is A=l*b.

4. The width of the rectangle comparing it to the area.

5. The process of rewriting the polynomial as a product of polynomial factors.