Question

Factor by Grouping
In the following exercises, factor by grouping.

$r^2-3r-r+3$.

Short answer

The obtained factors for the given expression $r^2-3r-r+3$ by using the grouping method are,$\left(r-3\right)\left(r-1\right)$.

Step-by-step solution

Given expression is,

$r^2-3r-r+3$.

The objective is, we need to find the factors for the given expression by using the grouping method.

First group the terms with the common factors.

$r^2-3r-r+3=(r^2-3r)+(-r+3)$

Now factor out the common factors.

$$\begin{gathered} r^2-3r-r+3=r\left(r-3\right)-1\left(r-3\right) \\ =\left(r-3\right)\left(r-1\right) \end{gathered}$$

The obtained factors are,$\left(r-3\right)\left(r-1\right)$.

Step 3 Let us check the answer by multiplying the factors.

$$\begin{gathered} \left(r-3\right)\left(r-1\right)=r^2-r-3r+3 \\ =r^2-3r-r+3 \end{gathered}$$

which is true.