Answer:
C. (3x – 1)(2x + 5)
Explanation:
To factor the trinomial 6x^2 + 13x - 5, we need to find two binomial factors whose product equals the given trinomial.
We can start by looking for two numbers that multiply to give the product of the coefficient of x^2, 6, and the constant term, -5. The product is -30.
We need to find two numbers that add up to the coefficient of x, which is 13.
After trying different combinations, we find that the numbers 15 and -2 satisfy these conditions. They multiply to -30 and add up to 13.
Now, we can rewrite the middle term 13x as 15x - 2x:
6x^2 + 15x - 2x - 5
Next, we group the terms and factor by grouping:
(6x^2 + 15x) + (-2x - 5)
Taking out the common factor from the first group and the second group:
3x(2x + 5) - 1(2x + 5)
Notice that we now have a common binomial factor, (2x + 5), which we can factor out:
(2x + 5)(3x - 1)
Therefore, the factored form of the trinomial 6x^2 + 13x - 5 is (3x - 1)(2x + 5).