Question

describe a situation involving area in square feet that can be modeled using the function g(x) = 2x^2 − 13x + 6

Answer 1

Area equals length times width
If you factor the binomial..
g(x)=(2x-1)(x-6)
Then the longer side length can be (2x-1) and width can be (x-6) of a rectangular area g(x).

Answer 2

Rectangle

Explanation:

Given is a polynomial in x of second degree as

`g(x) = 2x^2 − 13x + 6`

representing area in square feet.

Let us check whether we can factorise the polynomial

We can split middle term as 12 and 1

`g(x) = 2x^2 − 12x-x + 6\\=2x(x-6)-1(x-6)\\=(2x-1)(x-6)`

Thus the polynomial is a product of two factors

Hence the area represents area of a rectangle with length = 2x-1 and width = x-6