Factoring By Grouping

Students will be able to factor polynomials by grouping.

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Steps in Factoring Polynomials

• The first step in factoring a polynomial is to look for a common monomial factor.

• If you find a GCF, extract it, as we did in the last section.

• The next step is to look for a binomial factor, and extract it.

• How do you find a binomial factor?

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Finding a binomial factor

Follow these steps to find a binomial factor:

1. Group the terms in the polynomial into pairs with a common factor.

2. Extract the GCF from each pair of terms.

3. If the binomials remaining for each pair are identical, that is the binomial factor.

4. The monomials that have been extracted create a second polynomial.

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Example 1

Find the factors for 2a2 + 4ab + 3a + 6b1. Group:

2. Find GCF for each group.

The GCF for (2a2 + 4ab) is

The GCF for (3a + 6b) is

3. Extract GCF from each pair.

2a (a + 2b) + 3(a + 2b)

3. Extract binomial factor

(2a2 + 4ab) + (3a + 6b)

(a + 2b)(2a + 3)

2a

3

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Example 2

Find the factors for 4x3 + 4x2y2 – xy – y3

1. Group:

2. Find GCF for each group.

The GCF for (4x3 + 4x2y2) is

The GCF for (xy + y3) is

3. Extract GCF from each pair.

4x2 (x + y2) – y(x + y2)

4. Extract binomial factor

(4x3 + 4x2y2) – (xy + y3)

(x + y2)(4x2 – y)

4x2

y

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Example 3

Find the factors for

2x3 – 2x2y – 3xy2 + 3y3 + xz2 – yz2

(2x3 – 2x2y) – (3xy2 – 3y3) + (xz2 – yz2)

2x2(x – y) – 3y2(x – y) + z2(x – y)

(x – y) (2x2 – 3y2 + z2)