Question

A rectangular swimming pool has a positive area represented by the equation, A(x) = 2x^2 - x - 28 a. **Write two expressions in terms of x that could represent the length and width of the swimming pool. Hint: Factor the expression. Length: Width:

Answer 1

$A(x)=2x^2-x-28$$\Rightarrow A(x)=2x^2+7x-8x-28$$\Rightarrow A(x)=x(2x+7)-4(2x+7)$$\Rightarrow A(x)=(x-4)(2x+7)$

For positive values of x,

2x > x

Therefore

2x + 7 > x - 4

Hence,

the length could be 2x + 7

and width x - 4

Length: 2x + 7

width: x - 4