FACTORING COMMON MONOMIAL FACTOR

Factor out the greatest common monomial factor.

Problem 1 :

6x + 3

Solution :

= 6x + 3

= 2 ⋅ 3 ⋅ x + 3

Factoring 3, we get

= 3(2x + 1)

Problem 2 :

24x² - 8x

Solution :

= 24x² - 8x

= 3 ⋅ 8 ⋅ x ⋅ x - 8 ⋅ x

Factoring 8x, we get

= 8x(3x - 1)

Problem 3 :

6x - 12

Solution :

= 6x - 12

= 6 ⋅ x - 2 ⋅ 6

Factoring 6, we get

= 6(x - 2)

Problem 4 :

2x² + 8x

Solution :

= 2x² + 8x

= 2 ⋅ x ⋅ x + 2 ⋅ 4 ⋅ x

Factoring 2x, we get

= 2x (x + 4)

Problem 5 :

4x + 10

Solution :

= 4x + 10

= 2 ⋅ 2 ⋅ x + 2 ⋅ 5

Factoring 2 out, we get

= 2(2x + 5)

Problem 6 :

10x² + 35x

Solution :

= 10x² + 35x

= 2 ⋅ 5 ⋅ x² + 5 ⋅ 7 ⋅ x

Factoring 5x, we get

= 5x (2x + 7)

Problem 7 :

10x²y - 15xy²

Solution :

= 10x²y - 15xy²

= 2 ⋅ 5x²y - 3⋅ 5 xy²

Factoring 5xy, we get

= 5xy (2x - 3y)

Problem 8 :

12x² - 9x + 15

Solution :

= 12x² - 9x + 15

= 3 ⋅ 4x² - 3 ⋅ 3x + 3 ⋅ 5

Factoring 3, we get

= 3(4x² - 3x + 5)

Problem 9 :

3n³ - 12n² - 30n

Solution :

= 3n³ - 12n² - 30n

= 3 ⋅ n³ - 3 ⋅ 4n² - 3 ⋅ 10n

Factoring 3n, we get

= 3n (n² - 4n - 10)

Problem 10 :

 17x² + 34x + 51

Solution :

=  17x² + 34x + 51

= 17x² + 2 ⋅ 17 x + 3 ⋅ 17

Factoring 17, we get

= 17 (x² + 2 x + 3)

Problem 11 :

2x³ - 3x² + 5x

Solution :

= 2x³ - 3x² + 5x

Factoring x out, we get

= x(2x² - 3x + 5)

Problem 12 :

 13m + 26m² - 39m³

Solution :

= 13m + 26m² - 39m³

= 13 ⋅ m + 2 ⋅ 13m² - 3 ⋅ 13m³

= 13m(1 + 2m + 3m²)

Problem 13 :

(2r  - 4) / (r - 2)

Solution :

= (2r  - 4) / (r - 2)

Factoring 2 from the numerator, we get

= 2(r - 2) / (r - 2)

Cancelling the common factor, we get

= 2

Problem 14 :

45 / (10x - 10)

Solution :

= 45 / (10x - 10)

Factoring 5 from the denominator, we get

= 45 / 5(2x - 2)

= 9/(2x - 2)

Problem 15 :

(4n - 4) / (6n - 20) 

Solution :

= (4n - 4) / (6n - 20) 

Factoring 2 from the numerator and denominator, we get

= 2(2n - 2) / 2(3n - 10)

= (2n - 2) / (3n - 10)

Problem 16 :

(2n - 3) / (3 - 2n)

Solution :

Factoring negative from the numerator, we get

= -(3 - 2n) / (3 - 2n)

= -1

Problem 17 :

(6 - 8x)/(4x² - 3x)

Solution :

Factoring -2 from the numerator, we get

= 2(3 - 4x)/(4x² - 3x)

Factoring x from the denominator

= -2(4x - 3)/x(4x - 3)

By cancelling common factors, we get

= -2/x

Problem 18 :

(a² + 6a) / (ac + 6c)

Solution :

= (a² + 6a) / (ac + 6c)

Factoring a from the numerator and c from the denominator, we get

= a(a + 6) / c(a + 6)

= a/c

Problem 19 :

(x² + 4x) / (3x + 12)

Solution :

Factoring x from the numerator and 3 from the denominator, we get

= x(x + 4) / 3(x + 4)

Cancelling common factors, we get

= x/3

Problem 20 :

(15a - 3)/24

Solution :

= (15a - 3)/24

Factoring 3 from the numerator, we get

= 3(5a - 1) /24

= (5a - 1)/8