I would first factor out that 5: 15y^2-50y+35 = 5(3<span>y^2 - 10y + 7) and then focus on factoring </span>3y^2 - 10y + 7. Looking at the first and last coefficients 3 and 7, I'd form possible rational roots, which would include 7/3 and -7/3.
Using synthetic division, I'd determine whether either 7/3 or -7/3 is a root of 3y^2 - 10y + 7:
Since there is no remainder, I'd conclude that 7/3 is a root of 3y^2 - 10y + 7, and that (3x-7) is a factor. Look at the coefficients 3 -3; they tell us that (3x-3) is another factor.
Now let's take back that '5' we factored out earlier.
Factors of 15y^2 - 50y + 35 are 5, (3x-7) and (x-1).
Multiply these 3 factors together as a check. I found that (3x-7)(x-1) comes out to 3x^2 - 10x + 7, and that multiplying this by 5 produces
15y^2 - 50y + 35, which is the expression we started with.
Now we need to factor the trinomial. 3 can be factored as 3 * 1 7 can be factored as 1 * 7 or (-1) * (-7) Since the middle term is negative, we need to use -1 and -7 as the factors of 7
