A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? Explain the error.

Question

A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? Explain the error.

Student's work: 6x^2 - x - 12
6x^2 - 9x + 8x - 12
3x(2x-3)-4(-2x+3)
How can you tell that the student made an error when factoring? Explain the error.

Answer 1

The student made an error when factoring because the expression 6x^2 - 9x + 8x - 12 is not equivalent to the original expression 6x^2 - x - 12. The student incorrectly combined the terms 6x^2 and 8x, which should not be combined.

A student used factor by grouping to factor the expression below. How can you tell that the student made an error when​ factoring? Explain the error.

The student made an error when factoring because the expression 6x^2 - 9x + 8x - 12 is not equivalent to the original expression 6x^2 - x - 12. The student incorrectly combined the terms 6x^2 and 8x, which should not be combined.

A student used factor by grouping to factor the expression below. How can you tell that the student made an error when factoring? Explain the error.