– 4x3
Sol.
Dividend =
3x4 + 5x3 – 7x2 + 2x + 2
Divisor =
x2 + 3x + 1
x2 + 3x + 1
3x4 + 5x3 – 7x2 + 2x + 2
3x4
x2
=
3x2
(x2 + 3x + 1)
3x4
+
9x3
=
(–)
3x4
(–)
– 10x2
–
+ 2x
– 4x3
x2
=
– 4x
(x2 + 3x + 1)
– 4x3
–
12x2
– 4x
– 4x
=
– 4x3
(+)
2x2
+
(+)
2
+ 6x
2x2
x2
=
2
(x2 + 3x + 1)
2x2
+
6x
2
=
2x2
(–)
0
(–)
+ 2
Quotient =
Remainder =
3x2 – 4x + 2
0
∴
+ 9x3 + 3x2
– 12x2 – 4x
+ 2
+ 6x + 2
Exercise 2.3
Check whether the first polynomial is a factor of the second polynomial by
dividing the second polynomial by the first polynomial :
2.
(ii) 3x4 + 5x3 – 7x2 + 2x + 2, x2 + 3x + 1
+
3x2
–
4x
(+)
+
2
3x2
3x2
(–)
+
–
(–)
+
–
+
+ 2