Question

factor the polynomial.\\(x^2 + 3x - 4 = \square\\)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -4 (the constant term) and add up to 3 (the coefficient of the x term). The numbers are 4 and -1, since \(4\times(-1)= - 4\) and \(4+( - 1)=3\).

Step2: Factor the polynomial

Using the formula \(x^{2}+bx + c=(x + m)(x + n)\) where \(m\) and \(n\) are the two numbers we found, we get:
\(x^{2}+3x - 4=(x + 4)(x-1)\)

Answer:

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