Question

How do you factor `6d^2 + 35d - 6`?

Answer 1

Since there is a number in front of your x^2 term you would have to factor using the guess and check method. You could also divide all the terms by 6, but the 35/6 wouldn't be very fun to work with. Here's how you would do it using guess and check.

We know that we need to split this equation into two separate terms in parenthesis. For starters write this down:
(6d )(d )
(I already know that it won't be 2d and 3d in the parens.) Now that we have this, we look back at our first equation. What multiplies to -6? In this case we're looking for 6 and -1. So we put those into our parenthesis. We now have:
(6d-1)(d+6)
I'm going pretty fast so I hope you understand. If not, Khan academy has a great video here Factoring Trinomials
With our equation we now set each parenthesis equal to 0 and solve.

6d-1=0
d+6=0

So d=-6, and d=1/6

Answer 2

Factor: `y = 6d^2 + 35d - 6`

Ans: y = (6d - 1)(d + 6)

Explanation:

I use the new AC Method to factor trinomials (Socratic Search).
`y = 6d^2 + 35d - 6 =` 6(d + p)(d + q)
Converted trinomial `y' = d^2 + 35d - 36 =` (d + p')(d + q').
p' and q' have opposite signs. Factor pairs of (-36) --> (-1, 36) = 35 = b. Then p' = -1 and q' = 36.
Therefor, `p = (p')/a = -1/6` and `q = (q')/a = 36/6 = 6`
Factored form: `y = 6(d - 1/6)(d + 6) = (6d - 1)(d + 6).`