Factor the trinomial:3, x, squared, plus, 14, x, plus, 153x 2 +14x+15

To factor the trinomial 3x^2 + 14x + 15, follow these steps:

Step 1: Identify the coefficients and constant term. In this case, a = 3, b = 14, and c = 15.

Step 2: Look for two numbers that multiply to give ac (which is 315 = 45) and add up to b (which is 14). The numbers that satisfy these conditions are 5 and 9, because 59 = 45 and 5+9 = 14.

Step 3: Rewrite the middle term of the trinomial as the sum of the terms 5x and 9x. This gives us 3x^2 + 5x + 9x + 15.

Step 4: Factor by grouping. The first two terms can be factored as x(3x + 5), and the last two terms can be factored as 3(3x + 5).

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

So, the factored form of the trinomial 3x^2 + 14x + 15 is (3x + 5)(x + 3).