Question

Lillian has a rectangular garden with an area of 〖3x〗^2-10x-8 square feet. Find the expressions that would represent the length and width of the garden. Make sure you show all your work

Answer 1

The area of a garden is the amount of space on the garden

The length is x - 4 and the width is 3x + 2

How to determine the length and the width

The area of the garden is given as:

$Area = 3x^2 - 10x - 8$

Expand the equation

$Area = 3x^2 +2x- 12x - 8$

Factorize the above equation

$Area = x(3x +2) -4(3x +2)$

Factor out 3x + 2

$Area = (x-4) (3x +2)$

The area of the garden is the product of its dimension.

Hence, the length is x - 4 and the width is 3x + 2

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