91Ó°ÊÓ

When we talk about function evaluation, we refer to the process of finding the value of a function for a specific input. In this exercise, we have the function \( p(c) = c^2 + c \). We are tasked with finding \( p(-3) \), which means substituting \(-3\) into the function wherever there is a \(c\).
This provides us with the expression \((-3)^2 + (-3)\), which simplifies with basic arithmetic rules. The square of \(-3\) gives us \(9\) (because multiplying a negative number by itself results in a positive number).
Afterwards, we add \(9\) to \(-3\), resulting in \(6\). Therefore, \( p(-3) = 6 \).
This simple operation is the essence of function evaluation, showing how substitution allows us to evaluate functions at specific points.

Solving equations involves finding the values that satisfy a given equation. In this case, we need to solve the quadratic equation \( p(c) = 2 \) for \(c\).
Substitute the given value into the equation \( c^2 + c = 2 \), which means finding values of \(c\) that make this equation true. The first step is to rewrite the equation in standard form as \( c^2 + c - 2 = 0 \).
This rearrangement sets the stage for applying methods such as factoring or using the quadratic formula to find the solutions.
Finding these solutions helps determine where the function equals 2, which is a key skill in solving quadratic equations.

Factoring is a technique used to solve quadratic equations by expressing them as a product of simpler expressions. Here, we solved \( c^2 + c - 2 = 0 \) through factoring.
The goal is to write the quadratic as \((c - 1)(c + 2) = 0\), which means finding two numbers whose product gives the constant term (\