Question

the partial factorization of $x^2 - x - 12$ is modeled with algebra tiles. which unit tiles are needed to complete the factorization? \bigcirc 3 negative unit tiles \bigcirc 3 positive unit tiles \bigcirc 4 negative unit tiles \bigcirc 4 positive unit tiles

Explanation:

Step1: Factor the quadratic

We factor \(x^2 - x - 12\). We need two numbers that multiply to \(-12\) and add to \(-1\). The numbers are \(-4\) and \(3\), so \(x^2 - x - 12=(x + 3)(x - 4)\).

Step2: Analyze the algebra tiles

The top row has \(+x\) and three positive unit tiles (the \(+\) tiles). The left column has \(+x\). To complete the factorization, we look at the constant term. From the factored form \((x + 3)(x - 4)\), the constant part of the second binomial is \(-4\), which means we need 4 negative unit tiles to represent the \(-4\) (since unit tiles represent the constant term in the factorization model with algebra tiles).

Answer:

4 negative unit tiles (the option: 4 negative unit tiles)