Factoring by Grouping (Online Tutorial #19)

Factor by Grouping

Factoring by Grouping

Step by Step Guide

STEP ONE

Factor out the GCF of all four terms

STEP TWO

Group the first two terms together and then the last two terms together.

STEP THREE

Factor out the GCF from each separate binomial.

STEP FOUR

Factor out the common binomial.

STEP 5

Check whether any of your factors can be factored further.

STEP 6

If you factor and don't have a common binomial, then regroup your terms.

Multiple Choice

Factor: 6x² + 21x + 4x + 14

• (3x - 2)(2x - 7)

• 4(2x + 5)(3x - 4)

• (3x + 2)(2x + 7)

• 6(x + 2)(x - 7)

Multiple Choice

Factor by grouping:

4p³ + 8p² + 3p + 6

• (2p² + 3)(p + 2)

• (2p² + 6)(p + 4)

• (4p² + 3)(p + 2)

• (4p² + 8p)(3p + 6)

1. Always factor out the GCF first (if there is one)

2. Take the factors of a and c that ADD to make b

3. Rewrite b as a sum or difference (depending on the signs) of those factors.

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Factor by Grouping method:

Factor by Grouping

A polynomial can be factored by grouping only if these conditions exist:

• There are 4 or more terms

• Terms have common factors that can be grouped together

• There are two common factors that are identical or additive inverses of each other​

​

ax + bx + ay + by = (ax + bx) + (ay + by)

= x(a + b) + y(a + b)

= (x + y)(a + b)​

Some text here about the topic of discussion

Multiple Choice

Factor

3v² + 3v - 7v - 7

• (3v-7)(v+1)

• 3(v-7)(v-1)

• (3v+1)(v-9)

• (3v+1)(v-10)

Multiple Choice

Factor by grouping.

20x³ - 25x² + 4x - 5

• (5x² - 5)(4x + 1)

• 5(x² - 1)(4x + 5)

• (5x² + 1)(4x - 5)

• (5x² + 1)(4x - 1)

Multiple Choice

Factor:

6x² + 2x – 21x – 7

• (2x +7)(3x – 1)

• (1x – 1)(6x+7)

• (2x – 7)(3x+1)

• (6x – 7)(1x+1)