Question

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

Answer 1

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.

`1x^4 + 1x^3 + 0x^2 + 0x - 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 * 2 = 2`. Put it into the second column under the next `1` coefficient. We have:

`1`... `1` ... `0` ... `0`... `-1`
..... `2`

`1`

Now add 1 + 2.

`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.