Factor the trinomial:5, x, squared, plus, 32, x, plus, 355x 2 +32x+35

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

The trinomial is 5x^2 + 32x + 35.

Step 1: Identify a, b, and c in the trinomial ax^2 + bx + c Here, a = 5, b = 32, and c = 35.

Step 2: Find two numbers that multiply to ac (in this case, 535 = 175) and add up to b (in this case, 32). The numbers that satisfy this are 7 and 25 because 7*25 = 175 and 7 + 25 = 32.

Step 3: Rewrite the trinomial by breaking up the middle term using the two numbers found in step 2. So, 5x^2 + 32x + 35 becomes 5x^2 + 7x + 25x + 35.

Step 4: Factor by grouping. The first two terms can be grouped together and the last two terms can be grouped together like this: 5x(x + 7/5) + 5(5x + 7).

Step 5: Factor out the common factor. The common factor is (5x + 7), so the factored form of the trinomial is (5x + 7)(x + 5).

So, the factored form of the trinomial 5x^2 + 32x + 35 is (5x + 7)(x + 5).