+ x3
Sol.
Dividend =
x4 – 3x2 + 4x + 5
Divisor =
x2 + 1 – x
x4
=
x2 – x + 1
x4 + 0x3 – 3x2 + 4x + 5
x4
x2
=
x2
(x2 – x + 1)
x4
–
x3
=
(–)
x4
(–)
– 4x2
–
+ 4x + 5
x3
x2
=
x
(x2 – x + 1)
x3
–
x2
+ x
x
=
x3
(–)
– 3x2
+
(–)
2
+ 3x
–3x2
x2
=
–3
(x2 – x + 1)
–3x2
+
3x
–3
=
– 3x2
(+)
8
(+)
– 3
Quotient =
Remainder =
x2 + x – 3
8
∴
x2
=
– x
– x3 + x2
+ 0x3
– 3x2
+ 4x
+ 5
– x2 + x
+ 5
+ 3x – 3
+
+ 4x
– 3x2
x4
+ 5
x2
– x
Exercise 2.3
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and
remainder in each of the following :
1.
(ii) p(x) = x4 – 3x2 + 4x + 5, g(x) = x2 + 1 – x
+ 1
+ 1
+
x2
+
x
(+)
–
3
–
+
x2
x2
1
0
x
(+)
–
–
+
–
(–)
3 Marks –H.W.