7. Jason solved the quadratic equation x2−4x−12=0

Question

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

Answer 1

Question 7:

Jason's error occurred in Step 2. When he factored \( x^2 - 4x - 12 \), he should have factored it as \( (x - 6)(x + 2) \) correctly, but the mistake is that the product is incorrect: \( (x - 6)(x + 2) \) expands to \( x^2 - 4x - 12 \) correctly, but it implies incorrect roots when finding values that equal 0 in Step 3 and 4. He miscalculated the roots, leading to incorrect answers.

Question 8:

To solve the equation \( x^2 + 3x - 10 = 0 \) by factoring, we look for two numbers that multiply to \(-10\) (the constant term) and add to \(3\) (the coefficient of the linear term). The numbers \(5\) and \(-2\) fit these criteria.

Factoring the equation gives us: \[ (x + 5)(x - 2) = 0 \]

Setting each factor to zero gives us the solutions:

1. \( x + 5 = 0 \) → \( x = -5 \)
2. \( x - 2 = 0 \) → \( x = 2 \)

Therefore, the correct responses are:

• x = -5
• x = 2