. 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)

No drawing seen. Cannot copy and paste here.

To use the FOIL method to find the polynomial that represents the area of the square, we need to multiply the two binomials (2x+3) by itself.

FOIL stands for First, Outer, Inner, Last and is a method used to multiply two binomials.

The first step is to multiply the first terms of each binomial, which gives us 2x * 2x = 4x^2.

Next, we multiply the outer terms, which gives us 2x * 3 = 6x.

Then, we multiply the inner terms, which gives us 3 * 2x = 6x.

Finally, we multiply the last terms, which gives us 3 * 3 = 9.

Putting it all together, the polynomial that represents the area of the square is:
4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9.

Now, let's substitute x = 6 into the polynomial to find out if Victoria will have enough room to plant the garden.

When x = 6, we have:
4(6)^2 + 12(6) + 9 = 144 + 72 + 9 = 225.

So, the area of the square when x = 6 is 225 square units.

Since the area of the square is 225 square units and Victoria has a space allocated in her backyard that will accommodate 175 square feet, she will have enough room to plant the garden.