Final answer:
By using the Area model to multiply the expressions (x + 4) and (5x + 3), and adding the results from the four areas, we get the polynomial 5x^2 + 23x + 12, which is option c).
Step-by-step explanation:
To multiply the expressions (x + 4) and (5x + 3) using the Area model, we set up a rectangle divided into four smaller rectangles. Each side of the larger rectangle is divided into two parts: one for each term of the respective binomial.
In the top row, one smaller rectangle will represent the area (x * 5x) and another, the area (x * 3). In the bottom row, the corresponding smaller rectangles represent the areas (4 * 5x) and (4 * 3).
Multiplying the terms in each of the smaller rectangles, we get:
- x * 5x = 5x2
- x * 3 = 3x
- 4 * 5x = 20x
- 4 * 3 = 12
Adding these areas together (or adding the like terms), we get 5x2 + 3x + 20x + 12, which simplifies to 5x2 + 23x + 12.
Therefore, the answer to the multiplication of (x + 4)(5x + 3) using the Area model is 5x2 + 23x + 12, which corresponds to option c).