Answer:
(3x + 2) (4x + 3)
Step-by-step explanation:
Factoring 12x2 + 17x + 6
The first term is, 12x2 its coefficient is 12 .
The middle term is, +17x its coefficient is 17 .
The last term, "the constant", is +6
Step-1 : Multiply the coefficient of the first term by the constant 12 • 6 = 72
Step-2 : Find two factors of 72 whose sum equals the coefficient of the middle term, which is 17 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 8 and 9
12x2 + 8x + 9x + 6
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (3x+2)
Add up the last 2 terms, pulling out common factors :
3 • (3x+2)
Step-5 : Add up the four terms of step 4 :
(4x+3) • (3x+2)
Which is the desired factorization
Final result :
(-3x - 2) • (4x + 3)
