Final answer:
The trinomial 5a² - 4a - 28 can be factored by finding two numbers that multiply to -140 (5x-28) and add to -4. We find these numbers to be -8 and +7, leading to a factorization of (5a - 8)(a - 4), which is not listed among the options.
Step-by-step explanation:
To factor the trinomial 5a² - 4a - 28, we need to find two numbers that multiply to give the product of the coefficient of a² (which is 5) and the constant term (which is -28), and also add to give the coefficient of a (which is -4). The numbers that work here are -8 and +7. So, we can rewrite -4a as -8a + 7a.
5a² - 4a - 28 = 5a² - 8a + 7a - 28
Now we'll group the terms: (5a² - 8a) + (7a - 28) and factor by grouping.
5a² - 8a can be factored as a(5a - 8), and 7a - 28 can be factored as 7(a - 4). The trinomial factors into (5a - 8)(a - 4), which was not provided in the options, so this trinomial was incorrectly factored in the choices given to the student.