Factor the trinomial:3, x, squared, plus, 19, x, plus, 203x 2 +19x+20

The trinomial you provided is 3x^2 + 19x + 20. Here are the steps to factor it:

Step 1: Identify the coefficients and constant term. In this case, a = 3, b = 19, and c = 20.

Step 2: Look for two numbers that multiply to give ac (which is 320 = 60) and add up to give b (which is 19). The numbers that satisfy these conditions are 15 and 4 because 154 = 60 and 15 + 4 = 19.

Step 3: Rewrite the middle term of the trinomial as the sum of the terms 15x and 4x. This gives us 3x^2 + 15x + 4x + 20.

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^2 + 15x) + (4x + 20).

Step 5: Factor out the greatest common factor from each group. This gives us 3x(x + 5) + 4(x + 5).

Step 6: Notice that (x + 5) is a common factor. Factor out (x + 5), which gives us (3x + 4)(x + 5).

So, the factored form of the trinomial 3x^2 + 19x + 20 is (3x + 4)(x + 5).