Problem 20 - Elementary Algebra

Question

For the following problems, factor the trinomials when possible. $$ x^{2}+7 x+12 $$

Step-by-Step Solution

Answer

Answer: The factored form of the trinomial $$x^2 + 7x + 12$$ is $$(x + 3)(x + 4)$$.

Step 1: Identify the coefficients and constant term

In the given trinomial $$x^2 + 7x + 12$$, the coefficient of the quadratic term is 1, the coefficient of the linear term is 7, and the constant term is 12.

Step 2: Find two numbers that multiply to the constant term and add to the linear term's coefficient

We are looking for two numbers that multiply to 12 and add up to 7. These two numbers are 3 and 4 since (3)(4) = 12 and (3 + 4) = 7.

Step 3: Factor the trinomial into two binomials using the numbers found in step 2

Now we can factor the trinomial by substituting the numbers found in step 2 into two binomials. The factored form will be $$(x + 3)(x + 4)$$. So, the factored form of the given trinomial $$x^2 + 7x + 12$$ is $$(x + 3)(x + 4)$$.