Question

7. Jason solved the quadratic equation x2−4x−12=0
by factoring. His work is shown below.

Step 1: x2−4x−12=0
Step 2: (x-6)(x+2)=0

Step 3: x - 6 = 0, x + 2 = 0

Step 4: x = 6 or x = 2

Step 5: {6,2}

Jason plugged his solutions into the original equation, and found that they did not work. In which step did he first make a mistake?

(1 point)
Responses

Step 1
Step 1

Step 2
Step 2

Step 3
Step 3

Step 4
Step 4
Question 2
8. Solve for x by factoring x2+3x−10=0
. Select all that apply.(2 points)
Responses

x= -5
x= -5

x= -2
x= -2

x= -1
x= -1

x= 1
x= 1

x= 2
x= 2

x= 5
x= 5
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Answer 1

For the first question about Jason's solution to the quadratic equation \( x^2 - 4x - 12 = 0 \):

1. **Step 1**: He correctly writes the equation.
2. **Step 2**: The factorization (x - 6)(x + 2) is incorrect. The correct factorization should be (x - 6)(x + 2) = 0, which actually leads to the solutions \( x = 6 \) and \( x = -2 \). Therefore, Jason's first mistake occurs in **Step 2**.

So the correct response is **Step 2**.

Now for the second question regarding solving \( x^2 + 3x - 10 = 0 \) by factoring:

To factor \( x^2 + 3x - 10 \), we look for two numbers that multiply to -10 and add to 3. Those numbers are 5 and -2.

The factorization is:
\[ (x + 5)(x - 2) = 0 \]

Setting each factor to zero gives:
1. \( x + 5 = 0 \) → \( x = -5 \)
2. \( x - 2 = 0 \) → \( x = 2 \)

Thus, the solutions are \( x = -5 \) and \( x = 2 \).

The correct responses are:
- \( x = -5 \)
- \( x = 2 \)

Therefore, the correct answers are **x = -5** and **x = 2**.