Respuesta :
The model is a representation of the polynomial factors using algebraic
tiles.
The equation represented by the model is the option;
- [tex]\underline{x^2 - 4 \cdot x + 3 = (x - 3) \cdot (x - 1)}[/tex]
Reasons:
The parameters of the model of the polynomial and the factors of the
polynomial are;
The number of factors of the polynomial = 2
- Number of tiles in the factor 1 spot = 4 tiles, including;
1 of the four tiles is labelled x
3 of the four tiles is labelled -ve
Therefore;
A factor of the polynomial is x-tile, -tile, -tile, -tile = (x tile - 3 tiles) = (x - 3)
- Number of tiles in the factor 2 spot = 2 tiles which are;
1 of the two tiles is labelled x
1 of the two tiles is labelled -ve
Which gives;
A factor of the polynomial is x, -tile = (x-tile - 1 tile) = (x - 1)
- Number of tiles in the Product spot = 8 tiles
The 8 tiles are as follows;
1 of the 8 tiles is labelled x²
4 of the 8 tiles are labelled -x
3 of the 8 tiles are labelled +
Which gives;
The product of the polynomial is; (x²-tile - 4·x-tiles + 3-tiles) = (x² - 4·x + 3)
Multiplying the factors gives;
(x - 3) × (x - 1) = x² - 3·x - x + 4 = x² - 4·x + 3
The correct option is therefore;
- [tex]\underline{x^2 - 4 \cdot x + 3 = (x - 3)\cdot (x - 1)}[/tex]
The question options are;
x² - 2·x - 3 = (x - 3)·(x + 1)
x² - 4·x + 3 = (x - 3)·(x - 1)
x² + 2·x + 3 = (x + 3)·(x - 1)
x² + 4·x - 3 = (x + 3)·(x + 1)
Learn more about the factors of a polynomial here:
https://brainly.com/question/20294436
