Question

the factorization of $x^2 + 3x - 4$ is modeled with algebra tiles.
what are the factors of $x^2 + 3x - 4?$
$\bigcirc$ $(x + 4)$ and $(x - 4)$
$\bigcirc$ $(x + 3)$ and $(x - 4)$
$\bigcirc$ $(x + 4)$ and $(x - 1)$
$\bigcirc$ $(x + 3)$ and $(x - 1)$

Explanation:

Step1: Recall factoring quadratic formula

To factor \(x^2 + bx + c\), find two numbers that multiply to \(c\) and add to \(b\). For \(x^2 + 3x - 4\), find two numbers with product \(-4\) and sum \(3\).

Step2: Identify the numbers

The numbers \(4\) and \(-1\) work: \(4\times(-1)= -4\) and \(4 + (-1)=3\).

Step3: Write the factors

Thus, \(x^2 + 3x - 4=(x + 4)(x - 1)\).

Answer:

\((x + 4)\) and \((x - 1)\)