Divide Using Long Polynomial Division (y^4-3y^3+2y^2-20)÷(y^2+y-5)


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


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