The area of a rectangle is given by the product of its length and width. Therefore, we need to factor the given polynomial into two factors that represent the length and width of the table. We can do this by using the quadratic formula or by factoring the polynomial by grouping. Here, we will use factoring by grouping.
First, we group the terms in pairs:
7x^2 + 75x + 50 = (7x^2 + 35x) + (40x + 50)
Next, we factor out the greatest common factor from each pair of terms:
7x(x + 5) + 10(4x + 5)
We now have a common binomial factor of (x + 5), which we can factor out:
(7x + 10)(x + 5)
Therefore, the dimensions of the table are 7x + 10 and x + 5. We can check this by multiplying the dimensions:
(7x + 10)(x + 5) = 7x^2 + 35x + 10x + 50 = 7x^2 + 75x + 50
This confirms that the given polynomial represents the area of a rectangular table with dimensions of 7x + 10 and x + 5.