Question

Priscilla wants to replace the brick border around her rectangular swimming pool. The area of the pool is 3x^2 + 5x − 2. The total area of the brick and pool is 6x^2 − 21. How many square feet of brick does Priscilla need? (polynomials)

Answer 1

`(3x^2-5x-19)$ Square feet of brick`

Explanation:

`\text{The total area of the brick and pool }=6x^2 - 21\\\text{The area of the pool }= 3x^2 + 5x - 2. \\`

The total area of the brick and pool =Area of the Brick + Area of the Pool

Therefore:

Area of the Brick=Total area of the brick and pool-Area of the Pool

`=(6x^2 - 21)-(3x^2 + 5x - 2)\\=6x^2-21-3x^2-5x+2\\$Collect like terms\\=6x^2-3x^2-5x-21+2\\$Simplify\\=(3x^2-5x-19)$ Square feet`