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# Factoring by Grouping

## Use associative and commutative properties with factoring

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Practice Factoring by Grouping
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Factoring by Grouping

What if you had a polynomial expression like $3x^2 - 6x + 2x - 4$ in which some of the terms shared a common factor but not all of them? How could you factor this expression? After completing this Concept, you'll be able to factor polynomials like this one by grouping.

Fisch Video: Factoring Polynomials 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 $2x+2y+ax+ay$ .

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 $a$ . Factor 2 from the first two terms and factor $a$ from the last two terms:

$2x + 2y + ax + ay = 2(x + y) + a(x + y)$

Now we notice that the binomial $(x + y)$ is common to both terms. We factor the common binomial and get:

$(x + y)(2 + a)$

#### Example B

Factor $3x^2+6x+4x+8$ .

Solution

We factor 3x from the first two terms and factor 4 from the last two terms:

$3x(x+2)+4(x+2)$

Now factor $(x+2)$ from both terms: $(x+2)(3x+4)$ .

Now the polynomial is factored completely.

### Practice

Factor by grouping.

1. $6x^2-9x+10x-15$
2. $5x^2-35x+x-7$
3. $9x^2-9x-x+1$
4. $4x^2+32x-5x-40$
5. $2a^2-6ab+3ab-9b^2$
6. $5x^2+15x-2xy-6y$

### Additional Practice Opportunities (including self-check)

1. Braingenie: Factoring Polynomials by Grouping Terms