What is the factored form of the expression 6x^2+17x+12

(3x + 4) (2x + 3)

Step-by-step explanation:

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, that is

product = 6 * 12 = 72 and sum = + 17

The factors are + 8 and + 9

Use these factors to split the middle term

6x² + 8x + 9x + 12 (factor the first/second and third/fourth terms)

= 2x (3x + 4) + 3 (3x + 4) ← factor out (3x + 4)

= (3x + 4) (2x + 3) ← in factored form