Convert the expression x 2 +7x+12 to factor form.

To convert the expression x^2 + 7x + 12 to factor form, you need to factorize it. Here are the steps:

1. Identify the coefficients in the quadratic equation. In this case, a = 1 (coefficient of x^2), b = 7 (coefficient of x), and c = 12 (constant term).

2. Look for two numbers that multiply to give ac (in this case, ac = 112 = 12) and add up to give b (in this case, b = 7). The numbers that satisfy these conditions are 4 and 3 because 43 = 12 and 4+3 = 7.

3. Rewrite the middle term of the quadratic equation (7x) as the sum of the terms 4x and 3x. This gives us x^2 + 4x + 3x + 12.

4. Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us (x^2 + 4x) + (3x + 12).

5. Factor out the greatest common factor from each group. From the first group, we can factor out x, and from the second group, we can factor out 3. This gives us x(x + 4) + 3(x + 4).

6. Notice that the expressions in the parentheses are the same. We can factor out the common binomial term to get the final factored form of the equation: (x + 4)(x + 3).

So, the factor form of the expression x^2 + 7x + 12 is (x + 4)(x + 3).