# How do you divide (x^4+x^3-1)div(x-2) using synthetic division?

Jun 24, 2017

The key: don't leave out the "zero" terms.

#### Explanation:

Since ${x}^{4} + {x}^{3} - 1$ does not contain terms of every degree from its highest (4) to its lowest (0), we fill in the polynomial with placeholder terms that have coefficient zero.

$1 {x}^{4} + 1 {x}^{3} + 0 {x}^{2} + 0 x - 1$

Now, $x - 2$ is zero at x = 2. We use "2" in the synthetic division.

# 2

$1$... $1$ ... $0$ ... $0$... $- 1$

Bring down the "1" from the lead coefficient. After that, multiply by 2. $1 \cdot 2 = 2$. Put it into the second column under the next $1$ coefficient. We have:

$1$... $1$ ... $0$ ... $0$... $- 1$
..... $2$

$1$

$1$... $1$ ... $0$ ... $0$... $- 1$
..... $2$

$1$...$3$

Multiply by 2. Put it into the next column, and add:

$1$... $1$ ... $0$ ... $0$... $- 1$
..... $2$ ... $6$

$1$...$3$ ... $6$

At each step now, multiply by 2, put it into the next column, and add that column. You should put a 12 into the 4th column. I'll let you finish it. If you do it right, the last number in the last row will be a 23.