To factor the trinomial \(x^2 + x - 12\), we need to find two numbers that multiply to \(-12\) (the constant term) and add to \(1\) (the coefficient of the linear term).
The pairs of factors of \(-12\) are:
- \(1\) and \(-12\)
- \(-1\) and \(12\)
- \(2\) and \(-6\)
- \(-2\) and \(6\)
- \(3\) and \(-4\)
- \(-3\) and \(4\)
From these pairs, we see that \(4\) and \(-3\) add up to \(1\) (i.e., \(4 + (-3) = 1\)).
Thus, we can factor the trinomial as follows: \[ x^2 + x - 12 = (x + 4)(x - 3) \]
Therefore, the expression equivalent to the trinomial \(x^2 + x - 12\) is: \[ (x + 4)(x - 3) \]
Any presentation of this factorization (the order of the factors does not matter) will be correct; it could also be written as: \[ (x - 3)(x + 4) \]