Answer:
The width of the yard is given by the expression (x - 8).
Step-by-step explanation:
We are given the following in the question:
Area of yard, y =
[tex]y = x^2 - 12x + 32[/tex]
Length of garden =
[tex]x -4[/tex]
We have to find the with of the garden.
Area of yard =
[tex]\text{Length}\times \text{Width}[/tex]
Putting the values, we get:
[tex]x^2 - 12x + 32 = (x - 4) \times \text{Width}\\\\\text{Width} = \dfrac{x^2 - 12x + 32}{x-4}[/tex]
Now,
[tex]x^2 - 12x + 32 \\=x^2 - 8x - 4x + 32\\=x(x-8)-4(x-8)\\=(x-8)(x-4)[/tex]
[tex]\text{Width} = \dfrac{x^2 - 12x + 32}{x-4} = \dfrac{(x-8)(x-4)}{(x-4)} = x - 8[/tex]
Thus, the width of the yard is given by the expression (x - 8).
