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

Question

$(x-?)(x+?)=x^2+x-12$

00:00 Complete the appropriate numbers

00:03 Find the trinomial coefficients

00:14 We want to find 2 numbers whose product equals coefficient C

00:22 and their sum equals coefficient B

00:27 These are the appropriate numbers, let's substitute in the trinomial

00:31 And this is the solution to the question

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 $(x-3)(x+4)$ .

$\left(x-3\right)\left(x+4\right)$