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 :
x^{2} + 4x – 5x - 20
Solution :
Given, x^{2} + 4x – 5x – 20
By grouping,
= (x^{2} + 4x) + (-5x – 20)
By taking the common factor, we get
= x(x + 4) – 5(x + 4)
= (x + 4) (x – 5)
Problem 2 :
x^{2} - 7x + 3x - 21
Solution :
Given, x^{2} - 7x + 3x – 21
By grouping,
= (x^{2} - 7x) + (3x – 21)
By taking the common factor, we get
= x(x - 7) + 3(x - 7)
= (x - 7) (x + 3)
Problem 3 :
x^{2} - 3x + 2x - 6
Solution :
Given, x^{2} - 3x + 2x – 6
By grouping,
= (x^{2} - 3x) + (2x – 6)
By taking the common factor, we get
= x(x - 3) + 2(x - 3)
= (x - 3) (x + 2)
Problem 4 :
x^{2} - 6x - 3x + 18
Solution :
Given, x^{2} - 6x - 3x + 18
By grouping,
= (x^{2} - 6x) + (-3x + 18)
By taking the common factor, we get
= x(x - 6) - 3(x - 6)
= (x - 6) (x - 3)
Problem 5 :
x^{2} + 7x - 9x - 63
Solution :
Given, x^{2} + 7x - 9x – 63
By grouping,
= (x^{2} + 7x) + (-9x – 63)
By taking the common factor, we get
= x(x + 7) - 9(x + 7)
= (x + 7) (x - 9)
Problem 6 :
2x^{2} + x - 6x - 3
Solution :
Given, 2x^{2} + x - 6x – 3
By grouping,
= (2x^{2} + x) + (-6x – 3)
By taking the common factor, we get
= x(2x + 1) - 3(2x + 1)
= (2x + 1) (x - 3)
Problem 7 :
3x^{2} + 2x - 12x - 8
Solution :
Given, 3x^{2} + 2x - 12x – 8
By grouping,
= (3x^{2} + 2x) + (-12x – 8)
By taking the common factor, we get
= x(3x + 2) - 4(3x + 2)
= (3x + 2) (x - 4)
Problem 8 :
4x^{2} - 3x - 8x + 6
Solution :
Given, 4x^{2} - 3x - 8x + 6
By grouping,
= (4x^{2} - 3x) + (-8x + 6)
By taking the common factor, we get
= x(4x - 3) - 2(4x - 3)
= (4x - 3) (x - 2)
Problem 9 :
9x^{2} + 4x - 9x - 4
Solution :
Given, 9x^{2} + 4x - 9x + 6
By grouping,
= (9x^{2} + 4x) + (-9x + 6)
By taking the common factor, we get
= x(9x + 4) - 1(9x + 4)
= (9x + 4) (x - 1)
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