Answer:
2(2x + 1)(3x + 1)
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