Factor the trinomial:3, x, squared, plus, 10, x, plus, 33x 2 +10x+3

The trinomial you provided is 3x^2 + 10x + 3. Here are the steps to factor it:

Step 1: Identify the coefficients and constant term. In this case, a = 3, b = 10, and c = 3.

Step 2: Find two numbers that multiply to give ac (which is 33 = 9) and add to give b (which is 10). The numbers that satisfy these conditions are 9 and 1, because 91 = 9 and 9+1 = 10.

Step 3: Rewrite the middle term of the trinomial as the sum of the terms 9x and x. This gives us 3x^2 + 9x + x + 3.

Step 4: Factor by grouping. The first two terms can be factored as 3x(x + 3) and the last two terms can be factored as 1(x + 3).

Step 5: Since the terms in parentheses are the same, we can factor out the common factor of (x + 3) to get (3x + 1)(x + 3).

So, the factored form of the trinomial 3x^2 + 10x + 3 is (3x + 1)(x + 3).