Question

Tyra solved the quadratic equation x2-10x -24 = 0by factoring. Her work is shown below:

Step 1: x2-10x -24 = 0
Step 2: x2-4x - 6x - 24 = 0
Step 3: (x2-4x) + (-6x - 24) = 0
Step 4: x(x-4) - 6(x - 4)=0
Step 5: (x-4)(x-6)=0
Step 6: x-4 = 0, x-6 = 0
Step 7: x=4 or x = 6
Step 8: 4, 6

Tyra did not find the correct solutions. Investigate the steps, decipher her mistakes, and explain how to correct Tyra’s work.

Answer 1

The error in Tyra's factoring process was incorrect number selection; she should have used -12 and +2. The correct factored form of the quadratic equation is (x - 12)(x + 2) = 0, leading to the solutions x = 12 and x = -2.

Step-by-step explanation:

There is a mistake in Tyra's factoring process. When you factor the quadratic equation x² - 10x - 24, your goal is to find two numbers that multiply to -24 and add up to -10. The correct pair of numbers is -12 and +2, not -4 and -6 as Tyra used.

Therefore, the correct factoring should be:

• Step 1: x² - 10x - 24 = 0
• Step 2: x² - 12x + 2x - 24 = 0
• Step 3: (x² - 12x) + (2x - 24) = 0
• Step 4: x(x - 12) + 2(x - 12) = 0
• Step 5: (x - 12)(x + 2) = 0
• Step 6: x - 12 = 0 or x + 2 = 0
• Step 7: x = 12 or x = -2

The correct solutions to the original equation are x = 12 and x = -2.

Answer 2

Step 5 was not correct

Step-by-step explanation:

Tyra cannot take x and 6 common and then remove those valuse.