To factor the expression \(2x^2 + 7x - 30\), we can use the method of factoring by grouping.
1. **Multiply the coefficient of \(x^2\) (which is 2) by the constant term (which is -30):**
\[
2 \times -30 = -60
\]
2. **Next, we need to find two numbers that multiply to -60 and add to the coefficient of \(x\) (which is 7).**
The numbers are 12 and -5, since:
\[
12 \times -5 = -60 \quad \text{and} \quad 12 + (-5) = 7
\]
3. **Rewrite the middle term (7x) using these two numbers:**
\[
2x^2 + 12x - 5x - 30
\]
4. **Group the terms:**
\[
(2x^2 + 12x) + (-5x - 30)
\]
5. **Factor out the common factors in each group:**
\[
2x(x + 6) - 5(x + 6)
\]
6. **Now, factor out the common binomial factor \((x + 6)\):**
\[
(2x - 5)(x + 6)
\]
Thus, the factored form of \(2x^2 + 7x - 30\) is:
\[
(2x - 5)(x + 6)
\]
The correct response is:
\[
\text{left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 6 right parenthesis}
\]