Question

What would be the quickest way to multiply this polynomial? (x-3)(x+2)(x^2+3x-5)

Wolframalpha showed me this method but I do not know what it is called and how it works?

Answer 1

Below

Explanation:

The method that Wolfram alpha showed you isn't something that teachers would recommend. However, it is still pretty useful! I haven't seen it in a long time so I don't remember what this is called.

Basically what you would do is to multiply normally but instead you have some x's in your equation as well.

Your first row is:
`(x^2-x-6)times-5 = -5x^2+5x+30`

Your second row is:
`(x^2-x-6)times3x = 3x^3-3x^2-18x`

Your third row is:
`(x^2-x-6)times x^2 = x^4-x^3-6x^2`

Now all you have to do is line your rows up ie `x^2 "to" x^2, x^3 "to" x^3` so something like this

                 #-5x^2+5x+30# 
       #3x^3-3x^2-18x#
 #x^4-x^3-6x^2#

Once you've lined it all up, you can just add them together and you'll get your answer.

OR

you could honestly just add them all up like this:

`-5x^2+5x+30+3x^3-3x^2-18x+x^4-x^3-6x^2 = x^4+2x^3-14x^2-13x+30`