Question

1. $x^2 + x - 6$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-6\) (the constant term) and add up to \(1\) (the coefficient of \(x\)). The numbers are \(3\) and \(-2\) since \(3\times(-2)= -6\) and \(3+(-2)=1\).

Step2: Rewrite the middle term

Rewrite the quadratic expression \(x^{2}+x - 6\) as \(x^{2}+3x-2x - 6\).

Step3: Group and factor

Group the first two terms and the last two terms: \((x^{2}+3x)+(-2x - 6)\). Factor out the greatest common factor from each group: \(x(x + 3)-2(x + 3)\). Then factor out the common binomial factor \((x + 3)\) to get \((x + 3)(x - 2)\).

Answer:

\((x + 3)(x - 2)\)