1.

from here, the lowest power of x is 3, while of y is 5.. also, the coefficients have 4 as their highest common factor..

so you would have

if you set , then you will have , so that the one in the parenthesis would become , which is not factorable..

hence,

2.

notice that the factors of 15 are 1, 3, 5, 15 (positive and negative) and the factors of 8 are 1,2,4,8 (positive and negative)..

so what combinations of the factors of 15 and 8 that would give 14?? it is (5)(4) + (3)(-2) = 20 - 6..

(use the what so called FOIL method..)

thus you can factor to ..

3. do same as number two..

4.

so if you do FOIL method to every part, you should come up with

form here, you see that there are k+8, k+3, k+5 in both numerator and denominator, so that they would cancel out (assuming that they are not zzeros)

so, after cancellation, only factors left are k in the numerator and k-6 in the denominator.. therefore