Question

A rectangle has a height of 3c^4 and a width of c^2-4c+3. Express the area of the entire rectangle. Your answer should be a polynomial in standard form. The rectangle has 3 sections, one for each term of the width. what is the Area?

Answer 1

The area of the rectangle, given a height of 3c^4 and a width of c^2-4c+3, is calculated by multiplying these two expressions. The result in standard form is 3c^6 - 12c^5 + 9c^4.

Step-by-step explanation:

The area of a rectangle is calculated by multiplying its height by its width.

Given the height as 3c^4 and the width as c^2 - 4c + 3, the area A can be expressed as:

A = height × width = (3c^4) × (c^2 - 4c + 3)

To find the polynomial representing the area in standard form, we multiply each term of the width by the height:

A = 3c^4 × c^2 - 3c^4 × 4c + 3c^4 × 3

A = 3c^6 - 12c^5 + 9c^4

Therefore, the area of the rectangle as a polynomial in standard form is 3c^6 - 12c^5 + 9c^4.