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}
$
Friday, July 22, 2016
Beginning Algebra With Applications, Chapter 8, 8.1, Section 8.1, Problem 122
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