FACTORING EXPRESSIONS WITH FOUR TERMS

Step 1 :

If the given polynomial expressions with four terms, group the four terms into two pairs.

Step 2 :

Find the greatest common factor and take it out.

Step 3 :

Factor the common binomial out of the groups, the other factors will make the other binomial.

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)

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