Multiplying a Polynomial? (2x^2+x-1)(3x-2)

[janag35]

Hi,
I'm hoping you can help. This looks like a great site. I'm trying to multiply a polynomial and I'm trying to do it vertical.

I can't figure it out. I tried the F.O.I.L. method, but it doesn't appear to work with this problem. Please help.

(2x^2+x-1)(3x-2)

Thank you.

 

[tkhunny]

You have discovered the problem with "FOIL". It works ONLY for binomials.

Just learn to multiply - like you did long ago with numbers. Multiply each piece in one factor with each piece in the other. In your case,

(a+b+c)*(d+e) = (a+b+c)*d + (a+b+c)*e

It is hoped that you see how to proceed from there. It's called the Distributive Property of Multiplication over Addition.

 

[Denis]

One way is:

2x^2 + x - 1
3x - 2
====================
6x^3 + 3x^2 - 3x      : multiply by 3x
     - 4x^2 - 2x + 2  : multiply by -2
====================
Finish it!

 

[janag35]

Thank you. I recognized the way to multiply "downward" when you posted it. I also remember is is multiplying from left to right.

I appreciate your time, you help, and your quick responses.