Final answer:
To factor the expression 3sin^2x - 5sinx - 2, we can use the answer choices and check if they satisfy the conditions for factoring. Option A. (3sinx - 2)(sinx + 1) satisfies these conditions, and expanding it matches the original expression.
Step-by-step explanation:
To factor the expression 3sin^2x - 5sinx - 2, we need to find two binomials that when multiplied together will result in the given expression. The first term in each binomial will be a factor of 3sin^2x, and the last term in each binomial will be a factor of -2. The middle term in each binomial will be a combination of factors that add up to -5sinx. Looking at the answer choices, we can see that option A. (3sinx - 2)(sinx + 1) satisfies these conditions. To verify, we can use the distributive property to expand the expression and see if it matches the original expression. Expanding (3sinx - 2)(sinx + 1) gives us 3sin^2x - 2sinx + 3sinx - 2. Combining like terms, we get 3sin^2x - 5sinx - 2, which is the same as the original expression. Therefore, the correct answer is A. (3sinx - 2)(sinx + 1).