Factor completely. 6y^2-5y+1

Factor 6 y2 - 5y + 1 6 y2 - 5y + 1 = (3y - 1) (2y - 1) Answer: (3y - 1) (2y - 1)

Step-1 : Multiply the coefficient of the first term by the constant 6 • - 1 = - 6

Step-2 : Find two factors of - 6 whose sum equals the coefficient of the middle term, which is - 5.

-6 + 1 = - 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 1

6y2 - 6y + 1y - 1

Step-4 : Add up the first 2 terms, pulling out like factors:

6y • (y-1)

Add up the last 2 terms, pulling out common factors:

1 • (y-1)

Step-5 : Add up the four terms of step 4:

(6y+1) • (y-1)

Which is the desired factorization

Final result : (y - 1) • (6y + 1)