Solve (x-?)(x+?) = x²+x-12: Find the Missing Numbers in Factored Form

To solve this problem, we'll follow these steps:

• Step 1: Determine two numbers whose product is $-12$ (the constant term) and whose sum is $1$ (the coefficient of $x$).
• Step 2: Verify these numbers are $-3$ and $4$. Since $(-3) \times 4 = -12$ and $(-3) + 4 = 1$, both conditions are met.
• Step 3: Substitute these numbers into the expression $(x-?)(x+?)$ to get $(x-3)(x+4)$.
• Step 4: Double-check the factorization by expanding $(x-3)(x+4)$ to ensure it results in $x^2 + x - 12$.

Therefore, the factorized form of the given quadratic polynomial is $(x-3)(x+4)$.