5x^2 + kxy - 6y^2 + 13x - 5y + 6 are of the from (ax + by +c)(dx +ey +f): find k

[popcorn123]

The factors of p(x) = 5x^2 + kxy - 6y^2 + 13x - 5y + 6 are of the from (ax + by +c)(dx +ey +f) where all letters are integers. FIND K.

 

[stapel]

The factors of p(x) = 5x^2 + kxy - 6y^2 + 13x - 5y + 6 are of the from (ax + by +c)(dx +ey +f) where all letters are integers. FIND k.

Please reply with a clear listing of your thoughts and efforts so far. Thank you!

 

[popcorn123]

You posted 7 problems within a couple of minutes
and showed no work.
Can we have your teacher's email address in order
to confirm it's ok to do your homework...thank you.

I don't know of the email but we have a school email I'm sure. And you don't need to do the problems - cn you just help me see what needs to be done. I look at this and I try to factor and then I get stuck. I can't see anything else to do.

You don't need to do the problems- just like hints or something.

Thank you!

 

[stapel]

I try to factor and then I get stuck.

Please reply showing your efforts in this regard.

You don't need to do the problems- just like hints or something.

From what you know about multiplying polynomials, what must be the values of "a" and "d"?

From what you know about multiplying polynomials and the Rational Roots Test, what must be the list of possible value pairs for "c" and "f"?

Which terms, in the listed factors, multiply to -6y^2? So what must be the list of possible value pairs for "b" and "e"?

Starting from these restrictions, and testing possible pairs of factors, what can you find? (Yes, there may be a bit of guess-n-check for this exercise.)

If you get stuck, please reply showing what you've tried so far. Thank you!