Question

1. $x^{2}+x-42$

Explanation:

Step1: Identify quadratic form

The expression is $x^2 + x - 42$, a quadratic of the form $x^2+bx+c$.

Step2: Find factor pairs

Look for two numbers that multiply to $-42$ and add to $1$. These numbers are $7$ and $-6$, since $7\times(-6)=-42$ and $7+(-6)=1$.

Step3: Factor the quadratic

Rewrite the quadratic using the factor pair:
$x^2 + x - 42=(x+7)(x-6)$

Answer:

$(x+7)(x-6)$