Final answer:
After simplifying the student's expression to 5x - 54, the correct factors are found to be (x + 9)(x - 6), which shows that neither 2x - 9 nor 2x - 6 are factors of the expression 2x + 3x - 54.
Step-by-step explanation:
The factors of the expression 2x + 3x - 54 are found by first simplifying and then factoring the quadratic expression.
First, we combine like terms:
5x - 54
We then find two numbers that multiply to -54 and add to 5. These numbers are 9 and -6. The factored form of the expression is therefore:
(x + 9)(x - 6)
From this factorization, it's evident that the terms 2x - 9 and 2x - 6 are not true factors of the given expression. The correct factors of an expression are the terms that when multiplied together give the original expression. Since neither 2x - 9 nor 2x - 6 would yield the original expression when multiplied by an appropriate term, they cannot be considered as factors of 2x + 3x - 54.