Final answer:
The factors of the quadratic expression 5x^2 + 39x − 8 are (5x − 1) and (x + 8), which are found by breaking up the middle term using the numbers that multiply to the product of the coefficient of the x^2 term and the constant term, and add up to the coefficient of the x term. The correct answer is option: c) (5x − 1)(x 8).
Step-by-step explanation:
The student has asked for the factors of the quadratic expression 5x2 + 39x − 8. To factor this expression, we need to find two binomials whose product is the original expression. This is commonly done by trial and error or by using the AC method, where 'A' is the coefficient of the x2 term and 'C' is the constant term.
In this case, we look for two numbers that multiply to 5×(−8) = −40 (the product of A and C) and add up to 39 (the coefficient of the middle term, B).
The two numbers meeting these criteria are 40 and −1. So, we can break up the middle term into two terms using these numbers:
5x2 + 40x − x − 8
Now, we can factor by grouping:
(5x2 + 40x) + (−x − 8)
5x(x + 8) − 1(x + 8)
Finally, factoring out the common binomial factor (x + 8), we get:
(5x − 1)(x + 8)