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? _______________
To find the polynomial that represents the area of the square, we need to use the FOIL method. FOIL stands for First, Outer, Inner, Last, which refers to multiplying the terms of two binomials.
In this case, the binomial is (2x+3). To find the area of the square, we need to multiply this binomial by itself, as all sides of a square have the same length.
Using the FOIL method, we multiply the two binomials as follows:
First: (2x * 2x) = 4x^2
Outer: (2x * 3) = 6x
Inner: (3 * 2x) = 6x
Last: (3 * 3) = 9
Now we combine the results to form the polynomial:
4x^2 + 6x + 6x + 9 = 4x^2 + 12x + 9
So the polynomial that represents the area of the square is 4x^2 + 12x + 9.
To determine if Victoria has enough room to plant the garden when x=6, we substitute x=6 into the polynomial:
4(6^2) + 12(6) + 9
= 4(36) + 72 + 9
= 144 + 72 + 9
= 225
The result is 225 square feet. Since Victoria has allocated 175 square feet for her garden, she does not have enough room to plant the garden.