## About "How to factor polynomials with 4 terms by grouping"

How to factor polynomials with 4 terms by grouping :

Here we are going to see how to factor polynomials with 4 terms by grouping.

To factor polynomials with 4 terms by grouping, we need to split the given polynomial as two groups.

Factor out common term from the 1st and 2nd terms.

Factor out common term from the 3rd and 4th terms

## How to factor polynomials with 4 terms by grouping - Examples

Example 1 :

Factorize the following polynomial with grouping

x3 - 2x2 - x + 2

Solution :

=  x3 - 2x2 - x + 2

=  x2 (x - 2) - 1 (x - 2)

=  (x2 - 1)(x - 2)

=  (x2 - 12)(x - 2)

By comparing x2 - 1with the algebraic identity a2 - b, we get (x + 1) (x - 1)

=  (x + 1) (x - 1) (x - 2)

Hence the factors are (x + 1) (x - 1) (x - 2).

Example 2 :

Factorize the following polynomial with grouping

x3 + 3x2 - x - 3

Solution :

=  x3 + 3x2 - x - 3

In first two terms, we can factor out x2

In 3rd and fourth terms, we can factor out negative sign.

=  x2 (x + 3) - 1 (x + 3)

=  (x2 - 1) (x + 3)

By comparing x2 - 1with the algebraic identity a2 - b, we get (x + 1) (x - 1)

=  (x + 1) (x - 1) (x + 3)

Hence the factors are (x + 1) (x - 1) (x + 3).

Example 3 :

Factorize the following polynomial with grouping

x3 + x2 - 4x - 4

Solution :

=  x3 + x2 - 4x - 4

In first two terms, we can factor out x2

In 3rd and fourth terms, we can factor out -4.

=  x2 (x + 1) - 4 (x - 1)

=  (x2 - 4) (x + 1)

=  (x2 - 22) (x + 1)

By comparing x2 - 2with the algebraic identity a2 - b, we get (x + 2) (x - 2)

=  (x + 2) (x - 2) (x + 1)

Hence the factors are (x + 2) (x - 2) (x + 1).

Example 4 :

Factorize the following polynomial with grouping

x3 + 2x2 - x - 2

Solution :

=  x3 + 2x2 - x - 2

In first two terms, we can factor out x2

In 3rd and fourth terms, we can factor out negative sign.

=  x2 (x + 2) - 1 (x + 2)

=  (x2 - 1) (x + 2)

=  (x2 - 12) (x + 2)

By comparing x2 - 1with the algebraic identity a2 - b, we get (x + 1) (x - 1)

=  (x + 1) (x - 1) (x + 2)

Hence the factors are (x + 1) (x - 1) (x + 2).

Example 5 :

Factorize the following polynomial with grouping

x3 + 2x2 - x - 2

Solution :

=  x3 + 2x2 - x - 2

In first two terms, we can factor out x2

In 3rd and fourth terms, we can factor out negative sign.

=  x2 (x + 2) - 1 (x + 2)

=  (x2 - 1) (x + 2)

=  (x2 - 12) (x + 2)

By comparing x2 - 1with the algebraic identity a2 - b, we get (x + 1) (x - 1)

=  (x + 1) (x - 1) (x + 2)

Hence the factors are (x + 1) (x - 1) (x + 2).

Example 6 :

Factorize the following polynomial with grouping

x3 + 5x2 - x - 5

Solution :

=  x3 + 5x2 - x - 5

In first two terms, we can factor out x2

In 3rd and fourth terms, we can factor out negative sign.

=  x2 (x + 5) - 1 (x + 5)

=  (x2 - 1) (x + 5)

=  (x2 - 12) (x + 5)

By comparing x2 - 1with the algebraic identity a2 - b, we get (x + 1) (x - 1)

=  (x + 1) (x - 1) (x + 5)

Hence the factors are (x + 1) (x - 1) (x + 5).

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