Factor the following expression.

2 x squared plus 7 x minus 30
(1 point)
Responses

left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 6 right parenthesis
Image with alt text: left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 6 right parenthesis

left parenthesis 2 x minus 5 right parenthesis left parenthesis x minus 6 right parenthesis
Image with alt text: left parenthesis 2 x minus 5 right parenthesis left parenthesis x minus 6 right parenthesis

left parenthesis 2 x plus 5 right parenthesis left parenthesis x minus 6 right parenthesis
Image with alt text: left parenthesis 2 x plus 5 right parenthesis left parenthesis x minus 6 right parenthesis

left parenthesis 2 x plus 5 right parenthesis left parenthesis x plus 6 right parenthesis

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

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:
\[
\text{left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 6 right parenthesis}
\]