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

i think i am getting the hang of this. this is correct right?
x^3 + 6x^2 + 7x - 6

 

With a quick glance I think you're correct.

 

well, i multiplied everything in the left set by x. then by 3. and added the results all toghther...
thanks again

 

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

x^3 + 3x^2 + 3x^2 + 9x - 2x - 6

x^3 + 6x^2 + 7x - 6

yep.

 

Hey dude, do you know the "Horner's" system?

 

Hmm I don't think so. Sounds familiar though?

 

It's a method that what it practically does is the reverse of what we just did.
Meaning that x^3 + 6x^2 + 7x - 6 you can "deflate" thiis polynimial into a polyonimial with a smaller power. This polyonimial is 3rd power, with horner's method we can divide it in a polinimial with a power smaller by 1. Like this: (x^2 + 3x - 2)(x + 3)
I don't think you understood what I said because I said it complicated and might have said something wrong in there, but I was just checking if you know it.

 

Oh, yes, I do. This would involve synthetic/long division I think.

Going from a 3rd power to a 2nd power, or if it's a 5th power, down to a 4th power or lower. If the term (x+b) at the end is over 1, long division is required. If it's just 1 or 0, it can be synthetically simplified. Something like that?

 

Yeah, yeah that's it. Good.

 

I haven't used that method in a couple semesters so it's a bit foggy. I think I can still do it though if I tried hard enough. oh lulz