How do you divide (x^4+x^3-1)div(x-2)(x4+x3−1)÷(x−2) using synthetic division?

1 Answer
namralos
Jun 24, 2017

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

Explanation:

Since x^4 + x^3 - 1x4+x3−1 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 - 11x4+1x3+0x2+0x−1

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

# 2

1 1... 11 ... 00 ... 00... -1−1

Bring down the "1" from the lead coefficient. After that, multiply by 2. 1 * 2 = 21⋅2=2. Put it into the second column under the next 11 coefficient. We have:

1 1... 11 ... 00 ... 00... -1−1
..... 22

1 1

Now add 1 + 2.

1 1... 11 ... 00 ... 00... -1−1
..... 22

1 1...33

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

1 1... 11 ... 00 ... 00... -1−1
..... 22 ... 66

1 1...33 ... 66

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.

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