Find the Remainder 16x^3-5x+1 , x-1/4

,

Step 1
Divide the higher order polynomial by the other polynomial in order to find the remainder.

Step 2
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of .
-+-+

Step 3
Divide the highest order term in the dividend by the highest order term in divisor .
-+-+

Step 4
Multiply the new quotient term by the divisor.
-+-+
+-

Step 5
The expression needs to be subtracted from the dividend, so change all the signs in
-+-+
-+

Step 6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
-+-+
-+
+

Step 7
Pull the next terms from the original dividend down into the current dividend.
-+-+
-+
+-

Step 8
Divide the highest order term in the dividend by the highest order term in divisor .
+
-+-+
-+
+-

Step 9
Multiply the new quotient term by the divisor.
+
-+-+
-+
+-
+-

Step 10
The expression needs to be subtracted from the dividend, so change all the signs in
+
-+-+
-+
+-
-+

Step 11
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+
-+-+
-+
+-
-+
-

Step 12
Pull the next terms from the original dividend down into the current dividend.
+
-+-+
-+
+-
-+
-+

Step 13
Divide the highest order term in the dividend by the highest order term in divisor .
+-
-+-+
-+
+-
-+
-+

Step 14
Multiply the new quotient term by the divisor.
+-
-+-+
-+
+-
-+
-+
-+

Step 15
The expression needs to be subtracted from the dividend, so change all the signs in
+-
-+-+
-+
+-
-+
-+
+-

Step 16
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
+-
-+-+
-+
+-
-+
-+
+-

Step 17
Since the remander is , the final answer is the quotient.

Step 18
The remainder is the part of the answer that is left after the division by is complete.


Related Questions