## Grouping

**Grouping** is also called **triple common factoring**. It may be a better way to describe this technique.

Polynomials that can be grouped usually have four terms. Two terms can be common factored with one **greatest common factor (GCF)**, and the other two can be common factored with a different GCF. Then, the resulting polynomial will have a binomial GCF that can be common factored a third time.

For example: xy-2x+2y-4

We can see that the first two terms have a common factor of and the second two terms have a common factor of 2: x(y-2)+2(y-2)

Now, there is a (y-2) that can be common factored: (y-2)(x+2)

Be sure to common factor out a negative if the leading coefficient is negative. Otherwise, your two binomials will not be the same: \begin{array}{rl} & 6x^2+3x-14x-7\\ = & 3x(2x+1)-7(2x+1) \\ = & (2x+1)(3x-7) \end{array}

Always make sure that your polynomial is in descending order before grouping: \begin{array}{rl} & 4x+yz+4y+xz \\ = & xz+yz+4x+4y \\ = & z(x+y)+4(x+y) \\ = & (x+y)(z+4) \end{array}

### Practice

Simplify then evaluate: 2^{11} div 2^8

###### SOLUTION

Using the Law of Division: 2^{11} div 2^8=2^{11-8}=2^3

Evaluating: 2^3=8

Simplify: (m^0)^{10}

###### SOLUTION

Using the Law of Powers: (m^0)^{10}=m^0

We should more properly use the Law of Zero Exponents to write: m^0=1

Find the value of x that makes the equation true: 4^x times 4^4=4^7

###### SOLUTION

Since we are multiplying the two powers, we use the Law of Multiplication: x+4=7

Therefore: x=3

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