WOLFRAM|DEMONSTRATIONS PROJECT

Division of Polynomials up to Degree Six

​
p(x) =
c
6
6
x
+
c
5
5
x
+
c
4
4
x
+
c
3
3
x
+
c
2
2
x
+
c
1
x +
c
0
coefficients
c
6
4
c
5
6
c
4
6
c
3
5
c
2
3
c
1
6
c
0
4
q(x) =
a
6
6
x
+
a
5
5
x
+
a
4
4
x
+
a
3
3
x
+
a
2
2
x
+
a
1
x +
a
0
coefficients
a
6
0
a
5
4
a
4
2
a
3
4
a
2
1
a
1
2
a
0
4
reset
Divide the polynomial
p(x) = 4
6
x
+6
5
x
+6
4
x
+5
3
x
+3
2
x
+6x+4
by the polynomial
q(x) = 4
5
x
+2
4
x
+4
3
x
+
2
x
+2x+4
to get
p(x)
q(x)
=
R(x)
q(x)
+Q(x),
where degree R(x) < degree q(x).
Alternatively, this is
p(x)q(x)Q(x)+R(x).
The quotient is
Q(x) = x+1
and the remainder is
R(x) = 0.
​
This Demonstration divides two polynomials of degree six or less, showing the quotient and remainder.