What do you notice about the two problems below?

\[\frac{6x^3+13x^2+9x+2}{3x+2}= \ldots\]

\(\ldots x^2\) | \(\ldots x\) | \(\ldots\) | |
---|---|---|---|

\(3x\) | |||

\(+2\) |

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?