A student use 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:
2x^2+7x+6
2x^2 + x + 6x + 6
x(2x + 1) + 6(x + 1)
The error made by the student is in the second step of their work. They split the term 7x into 2 parts: 2x and 6x. However, the correct split should be 1x and 6x. So, the correct factored form should be:
2x^2 + 7x + 6
2x^2 + 1x + 6x + 6
x(2x + 1) + 3(2x + 2)
By comparing the student's work and the correct factored form, we can see that the student mistakenly split the term 7x incorrectly as 2x + 6x instead of 1x + 6x.