Question

factoring the polynomial 6x2-6xy-5x+5y

Answer 1

we know that since we have an x^2 that somewhere we need an x times x

(?x     ?)(?x     ?)

We also have 1 xy term so we know we need an x times a y

(?x   ?)(?x   ?y)

We just need to find the coefficents that make it work.  To get the 5y and the 5x we can really only have a 5 times a 1 because 5 is a prime number so we must have

(?x  5)(x   y)

That also tells us that the first coefficent must be 6 becasue 6x times x is 6x^2 and 6x times y is 6xy. So we have

(6x  5)(x  y)

Now we just need the proper signs.  Positive 6x times postive x is 6x^2

positive 6x times -y is -6xy

-5 times x is -5x

-5 times -y is 5y

so your answer is

(6x-5)(x-y)