The length and width of a rectangle are given by f(x) = 3x2 – 2x and g(x) = 2x – 3, where x > 2. What is f ⋅ g and what does its value represent?

A. (f ⋅ g)(x) = 12x2 – 40x + 33; the area of the rectangle
B. (f ⋅ g)(x) = 12x2 – 40x + 21; the perimeter of the rectangle
C. (f ⋅ g)(x) = 6x3 – 13x2 + 6x; the area of the rectangle
D. (f ⋅ g)(x) = 6x3 – 9x2 + 2x; the area of the rectangle

C

Step-by-step explanation:

We are multiplying f(x) and g(x), which are the length and width. The area of a rectangle is a=l*w, so we can eliminate choice B.

Now, we have to find what f(x) * g(x) is

 f(x) * g(x)

f(x) is 3x^2-2x and g(x) is 2x-3, so we can substitute them in

(3x^2-2x)*(2x-3)

Use FOIL to find the answer

F: 3x^2*2x= 6x^3

O: 3x^2* -3 = -9x^2

I: -2x*2x= -4x^2

L: -2x*-3= 6x

6x^3-9x^2-4x^2+6x

Combine like terms

6x^3-13x^2+6x

So, we know that f(x) *g(x) is 6x^3-13x^2+6x, and that it is the area (l*w), so choice C is correct.

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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