Question: II. Greatest Common Monomial Factor Factor, write prime if prime. 12a^3b + 15ab^3 = 3ab(4a^2 +…

II. Greatest Common Monomial Factor Factor, write prime if prime. 12a^3b + 15ab^3 = 3ab(4a^2 + 5b^2)

1. 6x + 3
2. 24x^2 - 8x
3. 6x - 12
4. 2x^2 + 8x
5. 4x + 10
6. 10x^2 + 35x
7. 10x^2y - 15xy^2
8. 12x^2 - 9x + 15
9. 3n^3 - 12n^2 - 30n
10. 9m^2 - 4n + 12
11. 2x^3 - 3x^2 + 5x
12. 13m + 26m^2 - 39m^3
13. 17x^2 + 34x + 51
14. 18m^2n^3 - 12m^2n^3 + 24m^2n^2

Solution

Here are the solutions for factoring each expression: 1. \(6x + 3\) Identify the greatest common factor: The GCF is 3. Factor it out: \[ 6x + 3 = 3(2x + 1) \] 2. \(24x^2 - 8x\) Identify the greatest common factor: The GCF is 8x. Factor it out: \[ 24x^2 - 8x = 8x(3x - 1) \] 3. \(6x - 12\) Identify the greatest common factor: The GCF is 6. Factor it out: \[ 6x - 12 = 6(x - 2) \] 4. \(2x^2 + 8x\) Identify the greatest common factor: The GCF is 2x. Factor it out: \[ 2x^2 + 8x = 2x(x + 4) \] 5. \(4x + 10\) Identify the greatest common factor: The GCF is 2. Factor it out: \[ 4x + 10 = 2(2x + 5) \] 6. \(10x^2 + 35x\) Identify the greatest common factor: The GCF is 5x. Factor it out: \[ 10x^2 + 35x = 5x(2x + 7) \] 7. \(10x^2y - 15xy^2\) Identify the greatest common factor: The GCF is 5xy. Factor it out: \[ 10x^2y - 15xy^2 = 5xy(2x - 3y) \] 8. \(12x^2 - 9x + 15\) Identify the greatest common factor: The GCF is 3. Factor it out: \[ 12x^2 - 9x + 15 = 3(4x^2 - 3x + 5) \] 9. \(3n^3 - 12n^2 - 30n\) Identify the greatest common factor: The GCF is 3n. Factor it out: \[ 3n^3 - 12n^2 - 30n = 3n(n^2 - 4n - 10) \] 10. \(9m^2 - 4n + 12\) No common factor; this expression is prime. 11. \(2x^3 - 3x^2 + 5x\) Identify the greatest common factor: The GCF is x. Factor it out: \[ 2x^3 - 3x^2 + 5x = x(2x^2 - 3x + 5) \] 12. \(13m + 26m^2 - 39m^3\) Identify the greatest common factor: The GCF is 13m. Factor it out: \[ 13m + 26m^2 - 39m^3 = 13m(1 + 2m - 3m^2) \] 13. \(17x^2 + 34x + 51\) Identify the greatest common factor: The GCF is 1 (no common factor other than 1). Factor it out: \[ 17x^2 + 34x + 51 = 1(17x^2 + 34x + 51) \] The expression is considered prime with respect to integer coefficients. 14. \(18m^7 - 12m^3 + 24m^2n^2\) Identify the greatest common factor: The GCF is 6m^2. Factor it out: \[ 18m^7 - 12m^3 + 24m^2n^2 = 6m^2(3m^5 - 2m + 4n^2) \]