1. ## Division With Polynomials

x 4 + 81 / x - 3

x 4 - 81 / x - 3

5x 3 - 12x 2 - 36x -16 /x + 2

x 5 - 8x 3 + 24x 2 + 12x + 40 / x + 4

x 4 - 3x 3 + 3x 2 - 3x + 6 /x - 2
I try to Dividing them but i all ways get them wrong and it say that i have to use Synthetic division

2. Study these examples: Synthetic Division

Then, try a few of yours and see how far you get.

3. Hello, frow4!

You're probably ignoring the "spaces" that are necessary . . .

$\displaystyle 3)\;\;(5x^3 - 12x^2 - 36x - 16) \div (x + 2)$
$\displaystyle \begin{array}{ccccccc} -2 & | & 5 & -12 & -36 & -16 \\ & | & & -10 & -44 & -16 \\ & & -- & -- & -- & -- \\ & & 5 & -22 & 8 & -32 \end{array}$

Answer: .$\displaystyle 5x^2 - 22x + 8 - \frac{32}{x+2}$

$\displaystyle 4)\;\;(x^5 - 8x^3 + 24x^2 + 12x + 40) \div (x + 4)$
Note that the dividend has no $\displaystyle x^4$ term.
We must think of it as: .$\displaystyle x^5 + {\color{blue}0\!\cdot\!x^4} - 8\!\cdot\!x^3 + 24\!\cdot\!x^2 + 12\!\cdot\!x + 40$

$\displaystyle \begin{array}{cccccccc} -4 & | & +1 & 0 & -8 & +24 & +12 & +40 \\ & | & & \text{-}4 & +16 & -32 & +32 & \text{-}176 \\ & & -- & -- & -- & -- & -- & -- \\ & & 1 & \text{-}4 & +8 & -8 & +44 & \text{-}136\end{array}$

Answer: .$\displaystyle x^4 - 4x^3 + 8x^2 - 8x + 44 - \frac{136}{x+4}$

$\displaystyle 2)\;\;(x^4 - 81) \div (x - 3)$
Note that: .$\displaystyle x^4 - 81 \;=\;x^4 + {\color{blue}0\!\cdot\!x^3 + 0\!\cdot\!x^2 + 0\!\cdot\!x} - 81$

$\displaystyle \begin{array}{ccccccc} 3 & | & 1 & 0 & 0 & 0 & \text{-}81 \\ & | & & 3 & 9 & 27 & 81 \\ & & -- & -- & -- & -- & -- \\ & & 1 & 3 & 9 & 27 & 0\end{array}$

Answer: .$\displaystyle x^3 + 3x^2 + 9x + 27$