8y^2 + 6y + 1
List the factors of a and c.
a: 1 x 8, 2 x 4
c: 1 x 1
Since c is positive find factors from the list that will add up to the absolute value of b.
1, 1, 2, and 4 -----> (1 x 2) + (1 x 4) = 6
Arrange these four factors accordingly. Because both b and c are positive, both parentheses will have a plus sign.
( + )( + )
Ask yourself, "Which two factors with y as a variable will multiply to give me 8y^2?" Fill in the parentheses.
(4y + )(2y + )
Use trial and error(by FOILing).
(4y + 1)(2y + 1)
Check answer.
(4y)(2y) = 8y^2
(4y)(1) = 4y
(2y)(1) = 2y
(1)(1) = 1
Set up as a polynomial.
8y^2 + 4y + 2y + 1
Combine like-terms.
8y^2 + 6y + 1
So 8y^2 + 6y + 1 is equal to (4y + 1)(2y + 1).