To factor the quadratic equation \(2x^2 + 7x - 15 = 0\), we need to find two numbers that multiply to \(2 \cdot -15 = -30\) and add up to \(7\).
The pairs of factors of \(-30\) that add to \(7\) are \(10\) and \(-3\). Therefore, we can rewrite the middle term \(7x\) as \(10x - 3x\):
\[ 2x^2 + 10x - 3x - 15 = 0 \]
Next, we can group the terms:
\[ (2x^2 + 10x) + (-3x - 15) = 0 \]
Factoring out the common factors from each group:
\[ 2x(x + 5) - 3(x + 5) = 0 \]
Now we can factor out the common binomial factor \((x + 5)\):
\[ (2x - 3)(x + 5) = 0 \]
The correctly factored form of the equation is:
\[ (2x - 3)(x + 5) = 0 \]
Thus, the correct choice is:
a (2x - 3)(x + 5) = 0
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