To factor the quadratic equation \( 2x^2 + 7x - 15 = 0 \), we will look for two numbers that multiply to \( 2 \cdot (-15) = -30 \) and add up to \( 7 \).
The numbers that satisfy these conditions are \( 10 \) and \( -3 \) since \( 10 \cdot (-3) = -30 \) and \( 10 + (-3) = 7 \).
Now, we can rewrite the quadratic equation:
\[ 2x^2 + 10x - 3x - 15 = 0 \]
Next, we will group the terms:
\[ (2x^2 + 10x) + (-3x - 15) = 0 \]
Now, factor by grouping:
\[ 2x(x + 5) - 3(x + 5) = 0 \]
This can be factored as:
\[ (2x - 3)(x + 5) = 0 \]
Thus, the correct factored form of the equation \( 2x^2 + 7x - 15 = 0 \) is:
\[ (2x - 3)(x + 5) = 0 \]
Therefore, the answer is:
A: \( (2x - 3)(x + 5) = 0 \).
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