Factor the trinomial:2, x, squared, plus, 11, x, plus, 142x 2 +11x+14

To factor the trinomial 2x^2 + 11x + 14, follow these steps:

1. Identify the coefficients and constant in the trinomial. Here, a = 2 (coefficient of x^2), b = 11 (coefficient of x), and c = 14 (constant).

2. Look for two numbers that multiply to give ac (a times c), and add up to give b. In this case, ac = 2 * 14 = 28 and b = 11. The numbers that fit this criteria are 7 and 4, since 7 * 4 = 28 and 7 + 4 = 11.

3. Rewrite the middle term (11x) as the sum of the terms 7x and 4x. This gives us 2x^2 + 7x + 4x + 14.

4. Factor by grouping. The first two terms (2x^2 + 7x) can be factored into x(2x + 7), and the last two terms (4x + 14) can be factored into 2(2x + 7).

5. Since the expressions in the parentheses are the same (2x + 7), we can factor them out to get (2x + 7)(x + 2).

So, the factored form of the trinomial 2x^2 + 11x + 14 is (2x + 7)(x + 2).