To find the dimensions of the rectangular swimming pool given that its area is \( x^2 + 2x - 15 \), we need to factor the quadratic expression.
First, we will factor \( x^2 + 2x - 15 \):
- Look for two numbers that multiply to \( -15 \) (the constant term) and add to \( 2 \) (the coefficient of the linear term).
The numbers that satisfy these conditions are \( 5 \) and \( -3 \), since:
- \( 5 \times (-3) = -15 \)
- \( 5 + (-3) = 2 \)
- Now we can write the expression in its factored form:
\[ x^2 + 2x - 15 = (x + 5)(x - 3) \]
Thus, the dimensions of the swimming pool are \( (x + 5) \) and \( (x - 3) \).
The correct choice from the provided options is:
(x + 5)(x - 3).
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