Divide Using Long Polynomial Division (x^4-2x^3-29x^2-43x+8)/(x-7)


Step 1
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
----+

Step 2
Divide the highest order term in the dividend by the highest order term in divisor .
----+

Step 3
Multiply the new quotient term by the divisor.
----+
+-

Step 4
The expression needs to be subtracted from the dividend, so change all the signs in
----+
-+

Step 5
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
----+
-+
+

Step 6
Pull the next terms from the original dividend down into the current dividend.
----+
-+
+-

Step 7
Divide the highest order term in the dividend by the highest order term in divisor .
+
----+
-+
+-

Step 8
Multiply the new quotient term by the divisor.
+
----+
-+
+-
+-

Step 9
The expression needs to be subtracted from the dividend, so change all the signs in
+
----+
-+
+-
-+

Step 10
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+
----+
-+
+-
-+
+

Step 11
Pull the next terms from the original dividend down into the current dividend.
+
----+
-+
+-
-+
+-

Step 12
Divide the highest order term in the dividend by the highest order term in divisor .
++
----+
-+
+-
-+
+-

Step 13
Multiply the new quotient term by the divisor.
++
----+
-+
+-
-+
+-
+-

Step 14
The expression needs to be subtracted from the dividend, so change all the signs in
++
----+
-+
+-
-+
+-
-+

Step 15
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
++
----+
-+
+-
-+
+-
-+
-

Step 16
Pull the next terms from the original dividend down into the current dividend.
++
----+
-+
+-
-+
+-
-+
-+

Step 17
Divide the highest order term in the dividend by the highest order term in divisor .
++-
----+
-+
+-
-+
+-
-+
-+

Step 18
Multiply the new quotient term by the divisor.
++-
----+
-+
+-
-+
+-
-+
-+
-+

Step 19
The expression needs to be subtracted from the dividend, so change all the signs in
++-
----+
-+
+-
-+
+-
-+
-+
+-

Step 20
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
++-
----+
-+
+-
-+
+-
-+
-+
+-
+

Step 21
The final answer is the quotient plus the remainder over the divisor.


Related Questions