Factor the trinomial:5, x, squared, plus, 31, x, plus, 305x 2 +31x+30

Sure, let's factor the trinomial step by step.

The trinomial is 5x^2 + 31x + 30.

Step 1: Identify a, b, and c in the trinomial ax^2 + bx + c In this case, a = 5, b = 31, and c = 30.

Step 2: Find two numbers that multiply to ac (in this case, 530 = 150) and add up to b (in this case, 31). The numbers that satisfy this are 10 and 15 because 10*15 = 150 and 10 + 15 = 31.

Step 3: Rewrite the trinomial by breaking up the middle term using the two numbers found in step 2. So, 5x^2 + 31x + 30 becomes 5x^2 + 10x + 15x + 30.

Step 4: Factor by grouping. The first two terms 5x^2 + 10x can be factored into 5x(x + 2) and the last two terms 15x + 30 can be factored into 15(x + 2).

Step 5: Since both terms now include (x + 2), we can factor that out to get: (x + 2)(5x + 15)

So, the factored form of the trinomial 5x^2 + 31x + 30 is (x + 2)(5x + 15).