Help with Synthetic Division

[digital pollen]

I have the problem in class and can't figure it out.. Could someone break the steps down for me please?

[marble fulcrum]

x^3 - 6x^2 + 11x - 6
well, you can add 0 to that
x^3 + 2x^2 - 2x^2 - 6x^2 + 11x - 6
and i did that to make the first 2 terms look like x + 2, but multiplied by something

so x^3 + 2x^2 - 8x^2 + 11x - 6
add 0 again
x^3 + 2x^2 - 8x^2 - 16x + 16x + 11x - 6

again, to make -8x^2 look like x + 2, it needs a -16x

x^3 + 2x^2 - 8x^2 - 16x + 27x - 6
add 0
x^3 + 2x^2 - 8x^2 - 16x + 27x + 54 - 54 - 6
so you would finally write it as
x^3 + 2x^2 - 8x^2 - 16x + 27x + 54 - 60

= x^2(x + 2) - 8x(x + 2) + 27(x + 2) - 60

= (x^2 - 8x + 27)(x + 2) - 60

this is basically long division, but like, without unnecessary symbols, imo

[digital pollen]

First of all wow that was fast.. Really appreciate that!

So you're not substituting the g(x) in the other x places?

it just tacs onto the end?