Equating coefficients

Students will learn how to determine the values of variables, in polynomial equations, by equating coefficients. To begin, students will learn that if two linear equations are equal for all \(x,\) then they must be the same line, and thus, they must have the same slope and \(y\)-intercept. Formally, if \(ax + b = cx + d,\) for all \(x,\) and \(a\) through \(d\) do not reference \(x,\) then \(a = c\) and \(b = d.\) Next, students will use this idea to solve problems.

After that, students will learn that the method of equating coefficients generalizes to polynomials of any degree. For example, if \(ax^2 + bx + c = dx^2 + ex + f,\) for all \(x,\) and \(a\) through \(f\) do not reference \(x,\) then \(a = d,\) \(b = e,\) and \(c = f.\)