Examples

x3-5x+6 , x+2
Step 1
Divide the higher order polynomial by the other polynomial in order to find the remainder.
x3-5x+6x+2
Step 2
Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of 0.
x+2x3+0x2-5x+6
Step 3
Divide the highest order term in the dividend x3 by the highest order term in divisor x.
x2
x+2x3+0x2-5x+6
Step 4
Multiply the new quotient term by the divisor.
x2
x+2x3+0x2-5x+6
+x3+2x2
Step 5
The expression needs to be subtracted from the dividend, so change all the signs in x3+2x2
x2
x+2x3+0x2-5x+6
-x3-2x2
Step 6
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x2
x+2x3+0x2-5x+6
-x3-2x2
-2x2
Step 7
Pull the next terms from the original dividend down into the current dividend.
x2
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
Step 8
Divide the highest order term in the dividend -2x2 by the highest order term in divisor x.
x2-2x
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
Step 9
Multiply the new quotient term by the divisor.
x2-2x
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
-2x2-4x
Step 10
The expression needs to be subtracted from the dividend, so change all the signs in -2x2-4x
x2-2x
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
Step 11
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x2-2x
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
-x
Step 12
Pull the next terms from the original dividend down into the current dividend.
x2-2x
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
-x+6
Step 13
Divide the highest order term in the dividend -x by the highest order term in divisor x.
x2-2x-1
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
-x+6
Step 14
Multiply the new quotient term by the divisor.
x2-2x-1
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
-x+6
-x-2
Step 15
The expression needs to be subtracted from the dividend, so change all the signs in -x-2
x2-2x-1
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
-x+6
+x+2
Step 16
After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.
x2-2x-1
x+2x3+0x2-5x+6
-x3-2x2
-2x2-5x
+2x2+4x
-x+6
+x+2
+8
Step 17
The final answer is the quotient plus the remainder over the divisor.
x2-2x-1+8x+2
Step 18
The remainder is the part of the answer that is left after the division by x+2 is complete.
8
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