25.9k views
2 votes
Factor the expression 3sin^2x - 5sinx - 2.

A. (3sinx - 2)(sinx + 1)
B. (3sinx + 2)(sinx - 1)
C. (3sinx - 1)(sinx + 2)
D. (3sinx + 1)(sinx - 2)

User Vasart
by
7.3k points

1 Answer

4 votes

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).

User Somasundaram Sekar
by
7.8k points

Related questions

asked Oct 15, 2023 147k views
Tavnab asked Oct 15, 2023
by Tavnab
7.8k points
1 answer
17 votes
147k views
asked Sep 25, 2021 100k views
Vsevolod Golovanov asked Sep 25, 2021
by Vsevolod Golovanov
7.1k points
1 answer
3 votes
100k views