FACTORING EXPRESSIONS WITH FOUR TERMS

Problem 1 :

x² + 4x – 5x - 20

Solution :

Given, x² + 4x – 5x – 20

By grouping,

= (x² + 4x) + (-5x – 20)

By taking the common factor, we get 

= x(x + 4) – 5(x + 4)

= (x + 4) (x – 5)

Problem 2 :

x² - 7x + 3x - 21

Solution :

Given, x² - 7x + 3x – 21

By grouping,

= (x² - 7x) + (3x – 21)

By taking the common factor, we get 

= x(x - 7) + 3(x - 7)

= (x - 7) (x + 3)

Problem 3 :

x² - 3x + 2x - 6

Solution :

Given, x² - 3x + 2x – 6

By grouping,

= (x² - 3x) + (2x – 6)

By taking the common factor, we get 

= x(x - 3) + 2(x - 3)

= (x - 3) (x + 2)

Problem 4 :

x² - 6x - 3x + 18

Solution :

Given,  x² - 6x - 3x + 18

By grouping,

= (x² - 6x) + (-3x + 18)

By taking the common factor, we get 

= x(x - 6) - 3(x - 6)

= (x - 6) (x - 3)

Problem 5 :

x² + 7x - 9x - 63

Solution :

Given, x² + 7x - 9x – 63

By grouping,

= (x² + 7x) + (-9x – 63)

By taking the common factor, we get 

= x(x + 7) - 9(x + 7)

= (x + 7) (x - 9)

Problem 6 :

2x² + x - 6x - 3

Solution :

Given, 2x² + x - 6x – 3

By grouping,

= (2x² + x) + (-6x – 3)

By taking the common factor, we get 

= x(2x + 1) - 3(2x + 1)

= (2x + 1) (x - 3)

Problem 7 :

3x² + 2x - 12x - 8

Solution :

Given, 3x² + 2x - 12x – 8

By grouping,

= (3x² + 2x) + (-12x – 8)

By taking the common factor, we get 

= x(3x + 2) - 4(3x + 2)

= (3x + 2) (x - 4)

Problem 8 :

4x² - 3x - 8x + 6

Solution :

Given, 4x² - 3x - 8x + 6

By grouping,

= (4x² - 3x) + (-8x + 6)

By taking the common factor, we get 

= x(4x - 3) - 2(4x - 3)

= (4x - 3) (x - 2)

Problem 9 :

9x² + 4x - 9x - 4

Solution :

Given, 9x² + 4x - 9x + 6

By grouping,

= (9x² + 4x) + (-9x + 6)

By taking the common factor, we get 

= x(9x + 4) - 1(9x + 4)

= (9x + 4) (x - 1)

Problem 10 :

Factor 5x³ + 25x² + 2x + 10

Solution :

= 5x³ + 25x² + 2x + 10

Factoring 5x² from first two terms and 2 from last two terms.

= 5x² (x + 5) + 2(x + 5)

= (5x² + 2) (x + 5)

Problem 11 :

Factor x³ + 2x² + 3x + 6

Solution :

= x³ + 2x² + 3x + 6

Factoring x² from first two terms and 3 from last two terms.

= x² (x + 2) + 3(x + 2)

= (x² + 3) (x + 2)

Problem 12 :

Factor x³ - 6x² + 4x - 24

Solution :

= x³ - 6x² + 4x - 24

Factoring x² from first two terms and 4 from last two terms.

= x² (x - 6) + 4(x - 6)

= (x² + 4) (x - 6)

Problem 13 :

Factor x³ - 4x² - 5x + 20

Solution :

= x³ - 4x² - 5x + 20

Factoring x² from first two terms and -5 from last two terms.

= x² (x - 4) - 5(x - 4)

= (x² - 5) (x - 4)

Problem 14 :

Factor x³ - 5x² - 2x + 10

Solution :

= x³ - 5x² - 2x + 10

Factoring x² from first two terms and -2 from last two terms.

= x² (x - 5) - 2(x - 5)

= (x² - 2) (x - 5)

Problem 15 :

Factor x³ + 4x² + 5x + 20

Solution :

= x³ + 4x² + 5x + 20

Factoring x² from first two terms and 5 from last two terms.

= x² (x + 4) + 5(x + 4)

= (x² + 5) (x + 4)

Problem 16 :

Factor x³ + 2x² - 3x - 6

Solution :

= x³ + 2x² - 3x - 6

Factoring x² from first two terms and -3 from last two terms.

= x² (x + 2) - 3(x + 2)

= (x² - 3) (x + 2)

Problem 17 :

Factor x³- 2x² - 5x + 10

Solution :

= x³- 2x² - 5x + 10

Factoring x² from first two terms and -5 from last two terms.

= x² (x - 2) - 5(x - 2)

= (x² - 5) (x - 2)

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