## About "Factoring polynomials with 4 terms by grouping worksheet"

Factoring polynomials with 4 terms by grouping worksheet :

Here we are going to see some practice questions on factoring polynomials with 4 terms by grouping.

## Factoring polynomials with 4 terms by grouping worksheet - Practice questions

(1)  Factorize the following polynomial with grouping

x3 - 2x2 - x + 2

(2)  Factorize the following polynomial with grouping

x3 + 3x2 - x - 3

(3)  Factorize the following polynomial with grouping

x3 + x2 - 4x - 4

(4)  Factorize the following polynomial with grouping

x3 + 2x2 - x - 2

(5)  Factorize the following polynomial with grouping

x3 + 2x2 - x - 2

(6)  Factorize the following polynomial with grouping

x3 + 5x2 - x - 5

## Factoring polynomials with 4 terms by grouping worksheet - Solution

Question 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).

Question 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).

Question 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).

Question 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).

Question 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).

Question 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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