Factor the trinomial:3, x, squared, plus, 23, x, plus, 303x 2 +23x+30

To factor the trinomial 3x^2 + 23x + 30, follow these steps:

Step 1: Identify the coefficients of the trinomial. Here, a = 3, b = 23, and c = 30.

Step 2: Look for two numbers that multiply to give ac (which is 330 = 90) and add up to b (which is 23). The numbers that satisfy these conditions are 15 and 6 because 156 = 90 and 15 + 6 = 23.

Step 3: Rewrite the middle term of the trinomial as the sum of the terms 15x and 6x. This gives us 3x^2 + 15x + 6x + 30.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us 3x(x + 5) + 6(x + 5).

Step 5: Notice that (x + 5) is a common factor. Factor out this term to get the final answer: (3x + 6)(x + 5).