Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 122

a. Which of the following expressions are equivalent to $x^2 - 5x + 6$?

I. $x^2 - 15x + 10x + 6$

II. $x^2 - x - 4x + 6$

III. $x^2 - 2x - 3x + 6$

All of the expressions are equivalent to $x^2 - 5x + 6$. Simplifying all the middle terms of each expression will give $x^2 - 5x + 6$.

b. Which expression in part a can be factored by grouping?

The expression $x^2 - 2x - 3x + 6$ can be factored by grouping. We have


$\begin{equation} \begin{aligned} x^2 - 2x - 3x + 6 =& (x^2 - 2x) - (3x-6) \\ =& x(x-2) - 3(x-2) \\ =& (x-3)(x-2) \end{aligned} \end{equation}$