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

1 Answer
Jun 24, 2017

Answer:

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.