12x²+x-6 solve using middle term
Answers
Answer:
(4x - 3) • (3x + 2)
Step-by-step explanation:
The first term is, 12x2 its coefficient is 12 .
The middle term is, -x its coefficient is -1 .
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 -1 .
-72 + 1 = -71
-36 + 2 = -34
-24 + 3 = -21
-18 + 4 = -14
-12 + 6 = -6
-9 + 8 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 8
12x2 - 9x + 8x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (4x-3)
Add up the last 2 terms, pulling out common factors :
2 • (4x-3)
Step-5 : Add up the four terms of step 4 :
(3x+2) • (4x-3)
Which is the desired factorization
Final result :
(4x - 3) • (3x + 2)