Answer: 3y+1
Step-by-step explanation: (((2•3y2) + y) - 2)
——————————————————— - 1
(2y - 1)
6y2 + y - 2
Simplify ———————————
2y - 1
Factoring 6y2 + y - 2
The first term is, 6y2 its coefficient is 6 .
The middle term is, +y its coefficient is 1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 6 • -2 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is 1 .
-12 + 1 = -11
-6 + 2 = -4
-4 + 3 = -1
-3 + 4 = 1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and 4
6y2 - 3y + 4y - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
3y • (2y-1)
Add up the last 2 terms, pulling out common factors :
2 • (2y-1)
Step-5 : Add up the four terms of step 4 :
(3y+2) • (2y-1)
Which is the desired factorization
2.2 Cancel out (2y-1) which appears on both sides of the fraction line.
Final result :
3y + 1