Lauren and Michael were working on the same math problem. Identify which student is incorrect and explain the error.
Lauren Michael
Solve: x² + x - 2 = 0 Solve: x² + x - 2 = 0
x² + 2x - x - 2 = 0 x² + 2x - x - 2 = 0
x(x + 2) -1(x + 2) = 0 x(x + 2) -1(x + 2) = 0
(x - 1)(x + 2) = 0 (x - 1)(x + 2) = 0
x = 1 or x = -2 x = -1 or x = 2
Lauren is incorrect. In the second step, she combined the x terms incorrectly. It should be x² + 2x - x - 2, which simplifies to x² + x - 2. The later steps are correct for both students.
To identify which student is incorrect, let's analyze their solutions step by step:
Lauren's Solution:
1. Starts with the equation: x² + x - 2 = 0
2. Combines like terms: x² + 2x - x - 2 = 0
3. Uses the distributive property to factor out common terms: x(x + 2) - 1(x + 2) = 0
4. Applies the difference of squares formula: (x - 1)(x + 2) = 0
5. Solves for x: x = 1 or x = -2
Michael's Solution:
1. Starts with the equation: x² + x - 2 = 0
2. Combines like terms: x² + 2x - x - 2 = 0
3. Uses the distributive property to factor out common terms: x(x + 2) - 1(x + 2) = 0
4. Applies the difference of squares formula: (x - 1)(x + 2) = 0
5. Solves for x: x = -1 or x = 2
Upon comparing their solutions, it can be seen that both Lauren and Michael arrived at the correct factored form of the equation, which is (x - 1)(x + 2) = 0. However, there is an error in Michael's final step of solving for x. Michael incorrectly listed the values of x as x = -1 or x = 2, which are not the correct solutions.
Hence, Michael is the student who is incorrect due to the error in stating the solutions for x.
The student who is incorrect is Lauren. When simplifying the equation, Lauren made an error in the step:
x(x + 2) - 1(x + 2) = 0
The correct step would be:
x(x + 2) - 1(x + 2) = 0
x^2 + 2x - x - 2 = 0
Lauren mistakenly distributed the -1 to both terms inside the parentheses. The correct distribution would be:
x^2 + 2x - 1(x + 2) = 0
x^2 + 2x - x - 2 = 0
Therefore, the error was made in the distribution of the -1.