Question

How do you factor the expression ${x^2} + x - 12$ ?

Answer 1

Hint: In the above problem you have to factor the expression ${x^2} + x - 12$. You can use the middle term factor to solve this problem. In the middle term factorization, we rewrite the middle term by adding or subtracting it in such a way that we can take common and find the factors. So let us see how we can solve this problem.

Complete step by step solution:
In the given problem, we have to find the factor of ${x^2} + x - 12$. Here, we will use the middle term factorization.
In ${x^2} + x - 12$ , +x can be written as 4x - 3x
 $\Rightarrow {x^2} + 4x - 3x - 12$
After taking common we get,
 $\Rightarrow x(x + 4) - 3(x + 4)$
 $\Rightarrow (x + 4)(x - 3)$

Therefore, the factor of ${x^2} + x - 12$ is $(x + 4)(x - 3)$

Additional Information:
The above solution used the formula of middle term factorization. A quadratic equation can be solved with the same formula. The quadratic equation is of different types: it can be a standard quadratic equation, factored form and vertex form.

Note:
In the above problem the equation was given but it did not equal to 0. It means that we do not have to find the value of x rather we have to check for the factors and find only the factors which will be our answer. On applying the middle term factorization we rewrite +x as 4x - 3x.