Final answer:
To factor the trinomial 5x² + 39x - 8, find two numbers that multiply to -40 and add up to 39. Those numbers are 40 and -1, therefore the trinomial factors into (5x - 1)(x + 8).
Step-by-step explanation:
To factor the trinomial 5x² + 39x - 8, we are looking for two binomials such that, when multiplied, they give us the original trinomial. This is a problem of searching for two numbers that multiply to give the product of the leading coefficient (5) and the constant term (-8), which is -40, and add up to the middle coefficient (39).
We can denote these two numbers as 'm' and 'n'. Upon inspection, the numbers that satisfy this are 40 and -1, because 40 * (-1) = -40 and 40 + (-1) = 39. Thus, the original trinomial can be factored as (5x - 1)(x + 8).