Factor the trinomial:2, x, squared, plus, 11, x, plus, 152x 2 +11x+15

To factor the trinomial 2x^2 + 11x + 15, follow these steps:

1. Identify the coefficients of the trinomial. In this case, a = 2, b = 11, and c = 15.

2. Look for two numbers that multiply to give ac (which is 215 = 30) and add up to b (which is 11). The numbers that satisfy these conditions are 5 and 6 because 56 = 30 and 5+6 = 11.

3. Rewrite the middle term of the trinomial as the sum of the terms 5x and 6x. This gives us 2x^2 + 5x + 6x + 15.

4. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us x(2x + 5) + 3(2x + 5).

5. Notice that (2x + 5) is a common factor. Factor out this term to get (2x + 5)(x + 3).

So, the factored form of the trinomial 2x^2 + 11x + 15 is (2x + 5)(x + 3).