Question

1. consider the equation ((2x + 2)^2 + 8(2x + 2) + 12 = 0). what substitution can we make to reduce this equation to a monic quadratic in the variable ( p )?

( p = ) enter your next step here

Explanation:

Step1: Identify repeated term

The equation has \(2x + 2\) repeated. Let \(p = 2x + 2\).

Step2: Substitute into equation

Substitute \(p\) into \((2x + 2)^2 + 8(2x + 2) + 12 = 0\), we get \(p^2 + 8p + 12 = 0\), which is a monic quadratic.

Answer:

\(p = 2x + 2\)