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)

Calculations:

Answer:_______________
Will she have enough room to plant the garden when x=6? _______________

(2*6+3)^2 > 175

15^2 > 175

225 > 175

To find the polynomial that represents the area of the square, we need to use the FOIL method.

The FOIL method is used to multiply two binomials together. In this case, the binomials are (2x+3) and itself.

FOIL stands for:
- First: Multiply the first terms of each binomial together.
- Outer: Multiply the outer terms of each binomial together.
- Inner: Multiply the inner terms of each binomial together.
- Last: Multiply the last terms of each binomial together.

Let's apply the FOIL method to (2x+3) multiplied by itself:

First: (2x)*(2x) = 4x^2
Outer: (2x)*(3) = 6x
Inner: (3)*(2x) = 6x
Last: (3)*(3) = 9

Now we can combine the terms to get the polynomial that represents the area of the square:

4x^2 + 6x + 6x + 9

Simplifying further, we get:

4x^2 + 12x + 9

Now that we have the polynomial, we can substitute x=6 to find out if Victoria will have enough room to plant the garden.

Replacing x with 6, we get:

4(6)^2 + 12(6) + 9
= 4(36) + 12(6) + 9
= 144 + 72 + 9
= 225

The result is 225 square feet.

Since the allocated space is 175 square feet and the calculated area is 225 square feet, Victoria will have enough room to plant the garden.