Victoria wants to plant a vegetable garden in the shape of a square. She has a space allocated in her backyard that will accommodate 175 square feet. Using the drawing below, use the FOIL method to find the polynomial that represents the area of the square. If x=6, will she have enough room to plant the garden? (2x+3)

The side is (2x+3)?

then the area is:
(2x+3)(2x+3) = 4 x^2 + 12 x + 9

if x = 6 then
Area = 4(36)+12(6)+9
= 144 + 72 + 9
= 225, too big :(

To find the polynomial that represents the area of the square, we'll use the FOIL method, which stands for First, Outer, Inner, Last.

1. First, multiply the first terms of each binomial: (2x) * (2x) = 4x^2.
2. Outer, multiply the outer terms of each binomial: (2x) * (3) = 6x.
3. Inner, multiply the inner terms of each binomial: (3) * (2x) = 6x.
4. Last, multiply the last terms of each binomial: (3) * (3) = 9.

Now, let's combine all the resulting terms:
4x^2 + 6x + 6x + 9.

Simplifying further:
4x^2 + 12x + 9.

Thus, the polynomial that represents the area of the square is 4x^2 + 12x + 9.

To determine if Victoria will have enough room to plant the garden, we need to substitute the value of x to see if the resulting area is less than or equal to the allocated space.

Given x = 6:
4(6)^2 + 12(6) + 9.

Simplifying further:
4(36) + 72 + 9
144 + 72 + 9 = 225.

Therefore, the area of the square is 225 square feet. If Victoria has allocated 175 square feet for the garden, she won't have enough room since 225 exceeds the allocated space.