### Polynomials & Rational Functions

Rich example

$\frac{6x^3+13x^2+9x+2}{3x+2}= \ldots$
How can you use the multiplication grid on the right-hand side to find the result of dividing $6x^3+13x^2+9x+2$ by $3x+2$?
What stays the same and what changes, if the division on the left-hand side is $\dfrac{6x^3+13x^2+9x+5}{3x+2}=\ldots$ instead?
Can you use a similar approach to divide $4x^4+3x^3+2x+1$ by $x^2+x+2$? Are you convinced that taking this approach gives you the same result as other methods?