The problem in the image asks to find the area of a rectangle and express it as a polynomial in standard form.

Given:

• The length of the rectangle is $5x - 5$.
• The width of the rectangle is 3.
• The variable $x = 1$ is mentioned, which might be for checking purposes, but it's not needed to find the polynomial.

Solution:

The area $A$ of a rectangle is given by the formula: $A = \text{length} \times \text{width}$

Substitute the given expressions: $A = (5x - 5) \times 3$

Now, distribute the 3 to both terms inside the parentheses: $A = 3(5x) - 3(5)$ $A = 15x - 15$

Thus, the area of the rectangle, expressed as a polynomial in standard form, is: $\boxed{15x - 15}$

Would you like to see more details about this calculation, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What would be the area if $x = 2$?
2. How does the area change as $x$ increases?
3. What are the length and width of the rectangle when $x = 0$?
4. How would the polynomial change if the width was $4$ instead of $3$?
5. How do you find the area of a rectangle when given algebraic expressions for length and width?

Tip: To simplify expressions like this, always distribute multiplication over addition or subtraction carefully.