What if you had a polynomial expression like \begin{align*}3x^2  6x + 2x  4\end{align*}
Fisch Video: Factoring Polynomials by Grouping
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CK12 Foundation: 0913S Factoring By Grouping
Guidance
Sometimes, we can factor a polynomial containing four or more terms by factoring common monomials from groups of terms. This method is called factor by grouping.
The next example illustrates how this process works.
Example A
Factor \begin{align*}2x+2y+ax+ay\end{align*}
Solution
There is no factor common to all the terms. However, the first two terms have a common factor of 2 and the last two terms have a common factor of \begin{align*}a\end{align*}
\begin{align*}2x + 2y + ax + ay = 2(x + y) + a(x + y)\end{align*}
Now we notice that the binomial \begin{align*}(x + y)\end{align*}
\begin{align*}(x + y)(2 + a)\end{align*}
Example B
Factor \begin{align*}3x^2+6x+4x+8\end{align*}
Solution
We factor 3x from the first two terms and factor 4 from the last two terms:
\begin{align*}3x(x+2)+4(x+2)\end{align*}
Now factor \begin{align*}(x+2)\end{align*}
Now the polynomial is factored completely.
Practice
Factor by grouping.

\begin{align*}6x^29x+10x15\end{align*}
6x2−9x+10x−15 
\begin{align*}5x^235x+x7\end{align*}
5x2−35x+x−7 
\begin{align*}9x^29xx+1\end{align*}
9x2−9x−x+1 
\begin{align*}4x^2+32x5x40\end{align*}
4x2+32x−5x−40 
\begin{align*}2a^26ab+3ab9b^2\end{align*}
2a2−6ab+3ab−9b2 
\begin{align*}5x^2+15x2xy6y\end{align*}
5x2+15x−2xy−6y
Additional Practice Opportunities (including selfcheck)
 Braingenie: Factoring Polynomials by Grouping Terms