What is 12x2+10x+2 factored completely?

2 (2x + 1) (3x + 1)

Step-by-step explanation:

given

12x² + 10x + 2 ← factor out 2 from each term

= 2 (6x² + 5x + 1) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term

product = 6 * 1 = 6, sum = + 5

The factors are + 3 and + 2

Use these factors to split the middle term

6x² + 3x + 2x + 1 (factor the first/second and third/fourth terms)

= 3x (2x + 1) + 1 (2x + 1) ← take out the common factor (2x + 1)

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

12x² + 10x + 2 = 2 (2x + 1) (3x + 1) ← in factored form