Question

Follow these steps to factor x^2 + 13x + 12.

a) (x + 1)(x + 12)

b) (x + 3)(x + 4)

c) (x + 6)(x + 2)

d) (x + 9)(x + 1)

Answer 1

The correct answer is A.

Answer 2

In order to factor x^2 + 13x + 12 is (x+1)(x+12). Option A is answer.

Step-by-step explanation:

Factoring a quadratic expression involves expressing it as a product of two binomials. In the case of x^2+13x+12, the factorization follows the sum-product pattern. By applying this pattern and simplifying, we arrive at the factored form (x+1)(x+12). This concise representation highlights the roots of the quadratic equation and, in this instance, leads us to identify Option A as the correct answer.

We can factor the expression x^2+13x+12 using the sum-product pattern, which states that the product of the sum of two numbers and their difference is equal to the difference of their squares.

Steps to solve:

1. Use the sum-product pattern:

x^2+13x+12 = x^2+12x+x+12

2. Extract the common factors:

x^2+13x+12 = x(x+12)+x+12

3. Rewrite in factored form:

x(x+12)+x+12 = (x+1)(x+12)

Option A is answer.