Factoring polynomials

mathinept · #1 $Old$ 09-06-2008, 02:26 PM

Hello,

I am trying to factor a polynomial 20y^2 + 39yx - 11x^2 but I can't seem to find two numbers that multiply to 220 and add to 39. I am sure there must be another pattern but can't find it in my notes or in my text! If someone could just show me the next step and explain it that would be great!

Thank you for your time,
Andrew

11rdc11 · #2 $Old$ 09-06-2008, 02:38 PM

ILoveMaths07 · #3 $Old$ 09-06-2008, 02:38 PM

Have you tried -5 and 44?

I hope that helps.

ILoveMaths07.

Matt Westwood · #4 $Old$ 09-06-2008, 02:40 PM

In this situation I tend to cheat, make it a quadratic in x/y or y/x (by dividing thru by x^2 or y^2) and then using the quadratic formula). Possibly cheating but when you do find the factors you don't have to admit to having used the formula to the teechur.

Soroban · #5 $Old$ 09-06-2008, 02:41 PM

Hello, Andrew!

Quote:

Factor: . $20y^2 + 39yx - 11x^2$
but I can't seem to find two numbers that multiply to 220 and add to 39. .?
You want a difference of 39 . . .

$220 \:=\:5\cdot44$

. . . $(5y + 11x)(4y - x)$

11rdc11 · #6 $Old$ 09-06-2008, 02:44 PM

Quote:

Originally Posted by Matt Westwood $View Post$

In this situation I tend to cheat, make it a quadratic in x/y or y/x (by dividing thru by x^2 or y^2) and then using the quadratic formula). Possibly cheating but when you do find the factors you don't have to admit to having used the formula to the teechur.

Thats how I tend to do it as well

mathinept · #7 $Old$ 09-06-2008, 02:48 PM

Thank you all for the help, and very fast too.